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The Minkowski inequalities for ( p , α ) $(p,alpha)$ -torsional rigidity and the extensions on Orlicz spaces (p, α)$ (p, α)$ -扭转刚度的Minkowski不等式及其在Orlicz空间上的扩展
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-18 DOI: 10.1002/mana.70032
Zhen-Hui Bu, Meng Qin, Denghui Wu
{"title":"The Minkowski inequalities for \u0000 \u0000 \u0000 (\u0000 p\u0000 ,\u0000 α\u0000 )\u0000 \u0000 $(p,alpha)$\u0000 -torsional rigidity and the extensions on Orlicz spaces","authors":"Zhen-Hui Bu,&nbsp;Meng Qin,&nbsp;Denghui Wu","doi":"10.1002/mana.70032","DOIUrl":"https://doi.org/10.1002/mana.70032","url":null,"abstract":"<p>In this paper, we prove the functional Minkowski inequality for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>α</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p,alpha)$</annotation>\u0000 </semantics></math>-torsional rigidity under suitable regularity assumptions, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>α</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p,alpha)$</annotation>\u0000 </semantics></math>-torsional rigidity can be formulated as the weak solution of an elliptic boundary value problem of the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplacian. We also establish the Orlicz Brunn–Minkowski and Orlicz Minkowski inequalities for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>α</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p,alpha)$</annotation>\u0000 </semantics></math>-torsional rigidity, which are extensions of the Brunn–Minkowski and Minkowski inequalities for torsional rigidity. Finally, we describe the equivalence between the Orlicz Brunn–Minkowski inequality and the Orlicz Minkowski inequality.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3191-3209"},"PeriodicalIF":0.8,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Resonances for vector-valued Jacobi operators on half-lattice 半格上向量值Jacobi算子的共振
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-17 DOI: 10.1002/mana.70026
Evgeny Korotyaev
{"title":"Resonances for vector-valued Jacobi operators on half-lattice","authors":"Evgeny Korotyaev","doi":"10.1002/mana.70026","DOIUrl":"https://doi.org/10.1002/mana.70026","url":null,"abstract":"<p>We study resonances for Jacobi operators on the half lattice with matrix-valued coefficients and finitely supported perturbations. We describe a forbidden domain, the geometry of resonances and their asymptotics when the main coefficient of the perturbation (determining its length of the support) goes to zero. Moreover, we show that \u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3075-3113"},"PeriodicalIF":0.8,"publicationDate":"2025-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An extension to a Liouville theorem on degenerate Monge–Ampère equations in half spaces 半空间中退化monge - ampatire方程的Liouville定理的推广
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-17 DOI: 10.1002/mana.70030
Xiaobiao Jia
{"title":"An extension to a Liouville theorem on degenerate Monge–Ampère equations in half spaces","authors":"Xiaobiao Jia","doi":"10.1002/mana.70030","DOIUrl":"https://doi.org/10.1002/mana.70030","url":null,"abstract":"<p>In this paper, we investigate the asymptotic behavior as infinity of a class of degenerate Monge–Ampère equations in half spaces. Meanwhile, we establish the Schauder estimates on a class of degenerate linear elliptic equations.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3156-3171"},"PeriodicalIF":0.8,"publicationDate":"2025-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Riemannian curvature identities for the torsion connection on Spin ( 7 ) ${rm Spin}(7)$ —Manifold and generalized Ricci solitons 自旋(7)$ {rm自旋}(7)$流形和广义Ricci孤子上扭转连接的黎曼曲率恒等
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-17 DOI: 10.1002/mana.12021
Stefan Ivanov, Alexander Petkov
{"title":"The Riemannian curvature identities for the torsion connection on \u0000 \u0000 \u0000 Spin\u0000 (\u0000 7\u0000 )\u0000 \u0000 ${rm Spin}(7)$\u0000 —Manifold and generalized Ricci solitons","authors":"Stefan Ivanov,&nbsp;Alexander Petkov","doi":"10.1002/mana.12021","DOIUrl":"https://doi.org/10.1002/mana.12021","url":null,"abstract":"&lt;p&gt;It is shown that on compact &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Spin&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;7&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Spin}(7)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-manifold with exterior derivative of the Lee form lying in the Lie algebra &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Spin&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;7&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Spin}(7)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; the curvature &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;annotation&gt;$R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Spin&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;7&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Spin}(7)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;–torsion connection &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Rin S^2Lambda ^2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with vanishing Ricci tensor if and only if the 3-form torsion is parallel with respect to the Levi-Civita connection. It is also proved that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;annotation&gt;$R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; satisfies the Riemannian first Bianchi identity exactly when the 3-form torsion is parallel with respect to the Levi-Civita and to the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Spin&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;7&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Spin}(7)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-torsion connections simultaneously. Precise conditions for a compact &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Spin&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;7&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Spin}(7)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-manifold to has closed torsion are given in terms of the Ricci tensor of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Spin&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;7&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"2906-2925"},"PeriodicalIF":0.8,"publicationDate":"2025-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Functions of self-adjoint operators under relatively bounded and relatively trace class perturbations 相对有界和相对迹类摄动下自伴随算子的函数
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-14 DOI: 10.1002/mana.70000
A. B. Aleksandrov, V. V. Peller
{"title":"Functions of self-adjoint operators under relatively bounded and relatively trace class perturbations","authors":"A. B. Aleksandrov,&nbsp;V. V. Peller","doi":"10.1002/mana.70000","DOIUrl":"https://doi.org/10.1002/mana.70000","url":null,"abstract":"<p>We study the behaviour of functions of self-adjoint operators under relatively bounded and relatively trace class perturbation. We introduce and study the class of relatively operator Lipschitz functions. An essential role is played by double operator integrals. We also consider the class of resolvent Lipschitz functions. Then we obtain a trace formula in the case of relatively trace class perturbations and show that the maximal class of function for which the trace formula holds in the case of relatively trace class perturbations coincides with the class of relatively operator Lipschitz functions. Our methods also give us a new approach to the inequality <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>∫</mo>\u0000 <mo>|</mo>\u0000 <mrow>\u0000 <mi>ξ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>|</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mo>+</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>t</mi>\u0000 <mo>|</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mspace></mspace>\u0000 <mi>d</mi>\u0000 <mi>t</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$int |bm{xi }(t)|(1+|t|)^{-1},{rm d}t&lt;infty$</annotation>\u0000 </semantics></math> for the spectral shift function <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ξ</mi>\u0000 </mrow>\u0000 <annotation>$bm{xi }$</annotation>\u0000 </semantics></math> in the case of relatively trace class perturbations.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3027-3048"},"PeriodicalIF":0.8,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Twistor spaces, conformal changes, and metric connections on the base manifold 扭转空间,共形变化,以及基本流形上的度量连接
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-11 DOI: 10.1002/mana.70020
Johann Davidov, Oleg Mushkarov
{"title":"Twistor spaces, conformal changes, and metric connections on the base manifold","authors":"Johann Davidov,&nbsp;Oleg Mushkarov","doi":"10.1002/mana.70020","DOIUrl":"https://doi.org/10.1002/mana.70020","url":null,"abstract":"<p>The following problems related to almost complex structures on a twistor space are discussed: (1) when two almost complex structures defined by a morphism of the twistor space and two conformal metrics on the base manifold coincide; (2) when the Atiyah–Hitchin–Singer or Eells–Salamon almost complex structures on the twistor space defined by two metric connections on the base Riemannian manifold coincide.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3049-3060"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimates for approximation characteristics of Nikol'skii–Besov classes of functions with mixed smoothness in the space B q , 1 ${B_{q,1}}$ 空间bq,1 ${B_{q,1}}$中混合光滑函数Nikol 'skii-Besov类的逼近特征估计
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-05 DOI: 10.1002/mana.70027
K. V. Pozharska, A. S. Romanyuk
{"title":"Estimates for approximation characteristics of Nikol'skii–Besov classes of functions with mixed smoothness in the space \u0000 \u0000 \u0000 B\u0000 \u0000 q\u0000 ,\u0000 1\u0000 \u0000 \u0000 ${B_{q,1}}$","authors":"K. V. Pozharska,&nbsp;A. S. Romanyuk","doi":"10.1002/mana.70027","DOIUrl":"https://doi.org/10.1002/mana.70027","url":null,"abstract":"&lt;p&gt;Exact-order estimates are obtained for some approximation characteristics of the classes of periodic multivariate functions with mixed smoothness (the Nikol'skii–Besov classes &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$B^{bm{r}}_{p, theta }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) in the space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$B_{q,1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$1 le p, q le infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$1le theta le infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, whose norm is stronger than the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$L_q$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-norm. It is shown that in the multivariate case (in contrast to the univariate) in most of the considered situations the obtained estimates differ in order from the corresponding estimates in the space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$L_q$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Besides, a significant progress is made in estimates for the considered approximation characteristics of the classes &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$B^{bm{r}}_{p, theta }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in the space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3114-3134"},"PeriodicalIF":0.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
L p - L q $L^ptext{-}L^q$ regularity of Forelli–Rudin-type operators on some bounded Hartogs domains 一些有界Hartogs域上forelli - rudin型算子的L p - L q$正则性
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-04 DOI: 10.1002/mana.12034
Enze Zhu, Qingyang Zou
{"title":"L\u0000 p\u0000 \u0000 -\u0000 \u0000 L\u0000 q\u0000 \u0000 \u0000 $L^ptext{-}L^q$\u0000 regularity of Forelli–Rudin-type operators on some bounded Hartogs domains","authors":"Enze Zhu,&nbsp;Qingyang Zou","doi":"10.1002/mana.12034","DOIUrl":"https://doi.org/10.1002/mana.12034","url":null,"abstract":"<p>This paper is concerned with a class of bounded pesudoconvex Hartogs domains, which is defined by the inequality\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"2986-3006"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Embeddings between sequence variable Lebesgue spaces, strict and finitely strict singularity 序列变量勒贝格空间之间的嵌入,严格和有限严格奇点
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-04 DOI: 10.1002/mana.12031
Jan Lang, Aleš Nekvinda
{"title":"Embeddings between sequence variable Lebesgue spaces, strict and finitely strict singularity","authors":"Jan Lang,&nbsp;Aleš Nekvinda","doi":"10.1002/mana.12031","DOIUrl":"https://doi.org/10.1002/mana.12031","url":null,"abstract":"&lt;p&gt;For two variable Lebesgue spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ℓ&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$ell _{p_n}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ℓ&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$ell _{q_n}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0&lt;p_n, q_n &lt;infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we provide necessary and sufficient conditions under which the natural embeddings &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ℓ&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ℓ&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$id:ell _{p_n} rightarrow ell _{q_n}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are strictly or finitely strictly singular. We also provide estimates for the Bernstein numbers of the natural embedding &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$id$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and show how they depend on the exponents &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$p_n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"2926-2941"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-isometric embeddings of C 0 ( K , X ) $C_{0}(K, X)$ spaces which induce isometries whenever X $X$ is a Hilbert space c0 (K, X)$ C_{0}(K, X)$空间的准等距嵌入,当X$ X$为希尔伯特空间时,可导出等距
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-08-04 DOI: 10.1002/mana.12033
Elói Medina Galego
{"title":"Quasi-isometric embeddings of \u0000 \u0000 \u0000 \u0000 C\u0000 0\u0000 \u0000 \u0000 (\u0000 K\u0000 ,\u0000 X\u0000 )\u0000 \u0000 \u0000 $C_{0}(K, X)$\u0000 spaces which induce isometries whenever \u0000 \u0000 X\u0000 $X$\u0000 is a Hilbert space","authors":"Elói Medina Galego","doi":"10.1002/mana.12033","DOIUrl":"https://doi.org/10.1002/mana.12033","url":null,"abstract":"<p>Suppose that <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> are locally compact Hausdorff spaces and <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> is a Hilbert space. It is proven that if there exist real numbers <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 <mo>≥</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$M ge 1$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>≥</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$L ge 0$</annotation>\u0000 </semantics></math> and a map <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> from <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>K</mi>\u0000 <mo>,</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$C_{0}(K,X)$</annotation>\u0000 </semantics></math> to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>S</mi>\u0000 <mo>,</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$C_{0}(S,X)$</annotation>\u0000 </semantics></math> satisfying\u0000\u0000 </p><p>In this case, as an immediate consequence, <span></span><math>\u0000 <semantics>\u0000 <mi>φ</mi>\u0000 <annotation>$varphi$</annotation>\u0000 </semantics></math> generates a linear isometry of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>K</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$C_{0}(K)$</annotation>\u0000 </semantics></math> into <span></span><math>\u0000 <semantics>\u0000 <mrow","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"2975-2985"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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