Mathematische Nachrichten最新文献

{"title":"Fractional Laplacian in V-shaped waveguide","authors":"Fedor Bakharev,&nbsp;Sergey Matveenko","doi":"10.1002/mana.202400271","DOIUrl":"https://doi.org/10.1002/mana.202400271","url":null,"abstract":"<p>The spectral properties of the restricted fractional Dirichlet Laplacian in <span>V</span>-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <msub>\u0000 <mi>Λ</mi>\u0000 <mo>†</mo>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mo>+</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$[Lambda _dagger, +infty)$</annotation>\u0000 </semantics></math> with the threshold corresponding to the smallest eigenvalue of the cross-sectional problems. In this work, the presence of a discrete spectrum at any junction angle is established along with the monotonic dependence of the discrete spectrum on the angle.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"427-436"},"PeriodicalIF":0.8,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397039","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}

{"title":"Seshadri constants on blow-ups of Hirzebruch surfaces","authors":"Krishna Hanumanthu,&nbsp;Cyril J. Jacob,&nbsp;B. N. Suhas,&nbsp;Amit Kumar Singh","doi":"10.1002/mana.202400018","DOIUrl":"https://doi.org/10.1002/mana.202400018","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$e,r ge 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be integers and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;⊕&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathbb {F}_e: = mathbb {P}(mathcal {O}_{mathbb {P}^1} oplus mathcal {O}_{mathbb {P}^1}(-e))$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denote the Hirzebruch surface with invariant &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;annotation&gt;$e$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We compute the Seshadri constants of an ample line bundle at an arbitrary point of the &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;-point blow-up of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$mathbb {F}_e$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; when &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;mi&gt;e&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$r le e-1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and at a very general point when &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;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$r=e$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; or &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 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"437-455"},"PeriodicalIF":0.8,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397040","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}

{"title":"Infinitely many low- and high-energy solutions for double-phase problems with variable exponent","authors":"Chun-Bo Lian,&nbsp;Qing-Hai Cao,&nbsp;Bin Ge","doi":"10.1002/mana.202300284","DOIUrl":"https://doi.org/10.1002/mana.202300284","url":null,"abstract":"<p>The aim of this paper is the study of double-phase problems with variable exponent. Using the Clark's theorem and the symmetric mountain pass lemma, we prove the existence of infinitely many small solutions and infinitely many large solutions, respectively.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"142-155"},"PeriodicalIF":0.8,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143114308","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}

{"title":"Multi-bump solutions for the nonlinear magnetic Schrödinger equation with logarithmic nonlinearity","authors":"Jun Wang,&nbsp;Zhaoyang Yin","doi":"10.1002/mana.202400134","DOIUrl":"https://doi.org/10.1002/mana.202400134","url":null,"abstract":"<p>In this paper, we study the following nonlinear magnetic Schrödinger equation with logarithmic nonlinearity\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"328-355"},"PeriodicalIF":0.8,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143114307","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}

{"title":"Realization of finite groups as isometry groups and problems of minimality","authors":"Pedro J. Chocano","doi":"10.1002/mana.202400287","DOIUrl":"https://doi.org/10.1002/mana.202400287","url":null,"abstract":"&lt;p&gt;A finite group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is said to be realized by a finite subset &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;annotation&gt;$V$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a Euclidean space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$mathbb {R}^n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; if the isometry group of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;annotation&gt;$V$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is isomorphic to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We prove that every finite group can be realized by a finite subset &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Vsubset mathbb {R}^{|G|}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; consisting of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"419-426"},"PeriodicalIF":0.8,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400287","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396770","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}

{"title":"Calderón–Zygmund theory on some Lie groups of exponential growth","authors":"Filippo De Mari,&nbsp;Matteo Levi,&nbsp;Matteo Monti,&nbsp;Maria Vallarino","doi":"10.1002/mana.202300499","DOIUrl":"https://doi.org/10.1002/mana.202300499","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>=</mo>\u0000 <mi>N</mi>\u0000 <mo>⋊</mo>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$G = N rtimes A$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> is a stratified Lie group and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mo>+</mo>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$A= mathbb {R}_+$</annotation>\u0000 </semantics></math> acts on <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> via automorphic dilations. We prove that the group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> has the Calderón–Zygmund property, in the sense of Hebisch and Steger, with respect to a family of flow measures and metrics. This generalizes in various directions previous works by Hebisch and Steger and Martini et al., and provides a new approach in the development of the Calderón–Zygmund theory in Lie groups of exponential growth. We also prove a weak-type (1,1) estimate for the Hardy–Littlewood maximal operator naturally arising in this setting.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"113-141"},"PeriodicalIF":0.8,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300499","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143111990","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}

{"title":"Disjoint \u0000 \u0000 p\u0000 $p$\u0000 -convergent operators and their adjoints","authors":"Geraldo Botelho,&nbsp;Luis Alberto Garcia,&nbsp;Vinícius C. C. Miranda","doi":"10.1002/mana.202300561","DOIUrl":"https://doi.org/10.1002/mana.202300561","url":null,"abstract":"&lt;p&gt;First, we give conditions on a Banach lattice &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;$E$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; so that an operator &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;annotation&gt;$T$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; from &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;$E$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to any Banach space is disjoint &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-convergent if and only if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;annotation&gt;$T$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is almost Dunford–Pettis. Then, we study when adjoints of positive operators between Banach lattices are disjoint &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-convergent. For instance, we prove that the following conditions are equivalent for all Banach lattices &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;$E$&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;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;: (i) a positive operator &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$T: E rightarrow F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is almost weak &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-convergent if and only if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$T^*$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is disjoint &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-convergent; (ii) &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$E^*$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has order continuous norm or &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$F^*$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has the positive Schur property of order &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4766-4777"},"PeriodicalIF":0.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862177","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}

{"title":"Existence and regularity of strict solutions for a class of fractional evolution equations","authors":"Guang Meng Wu,&nbsp;Jia Wei He","doi":"10.1002/mana.202400074","DOIUrl":"https://doi.org/10.1002/mana.202400074","url":null,"abstract":"<p>We study the existence and Hölder regularity of solutions for fractional evolution equations of order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$alpha in (1,2)$</annotation>\u0000 </semantics></math>. By means of an analytic resolvent, we construct an interpolation space, which can effectively lower the regularity of initial data. By virtue of the interpolation space and some properties of the analytic resolvent, we derive the existence and Hölder regularity of strict solutions for an inhomogeneous problem, as well as the existence and Hölder regularity of a nonlinear problem.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4730-4749"},"PeriodicalIF":0.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861998","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}

{"title":"Two-sided estimates of Lebesque constants for Hölder spaces","authors":"Evgenii I. Berezhnoi","doi":"10.1002/mana.202200286","DOIUrl":"https://doi.org/10.1002/mana.202200286","url":null,"abstract":"<p>A two-sided estimate of Lebesgue constants is proposed for the Hölder space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>H</mi>\u0000 <mi>k</mi>\u0000 <mi>ω</mi>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H_k^omega (X)$</annotation>\u0000 </semantics></math>, constructed from the modulus of continuity of the <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>th order calculated in the symmetric space <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. Choosing different function spaces <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>, we obtain new criteria for the convergence of classical Fourier series.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4750-4765"},"PeriodicalIF":0.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861999","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}

{"title":"Strong Kähler with torsion solvable lie algebras with codimension 2 nilradical","authors":"Beatrice Brienza,&nbsp;Anna Fino","doi":"10.1002/mana.202400349","DOIUrl":"https://doi.org/10.1002/mana.202400349","url":null,"abstract":"<p>In this paper, we study strong Kähler with torsion (SKT) and generalized Kähler structures on solvable Lie algebras with (not necessarily abelian) codimension 2 nilradical. We treat separately the case of <span></span><math>\u0000 <semantics>\u0000 <mi>J</mi>\u0000 <annotation>$J$</annotation>\u0000 </semantics></math>-invariant nilradical and non-<span></span><math>\u0000 <semantics>\u0000 <mi>J</mi>\u0000 <annotation>$J$</annotation>\u0000 </semantics></math>-invariant nilradical. A classification of such SKT Lie algebras in dimension 6 is provided. In particular, we give a general construction to extend SKT nilpotent Lie algebras to SKT solvable Lie algebras of higher dimension, and we construct new examples of SKT and generalized Kähler compact solvmanifolds.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4705-4729"},"PeriodicalIF":0.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400349","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861333","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}