Mathematische Nachrichten最新文献

筛选
英文 中文
On the Lyapunov exponents of triangular discrete time-varying systems 三角离散时变系统的Lyapunov指数
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-12 DOI: 10.1002/mana.202300373
Adam Czornik, Thai Son Doan
{"title":"On the Lyapunov exponents of triangular discrete time-varying systems","authors":"Adam Czornik,&nbsp;Thai Son Doan","doi":"10.1002/mana.202300373","DOIUrl":"https://doi.org/10.1002/mana.202300373","url":null,"abstract":"<p>In this paper, we present upper and lower estimates for the Lyapunov exponents of discrete linear systems with triangular time-varying coefficients. These estimates are expressed by the diagonal elements of the coefficient matrix. As a conclusion from these estimates, we also obtain bounds for the Grobman regularity coefficient.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"976-997"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595337","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
Rational cohomology of M 4 , 1 $mathcal {M}_{4,1}$ M $mathcal {M}_{4,1}$的有理上同
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-12 DOI: 10.1002/mana.202400294
Yiu Man Wong, Angelina Zheng
{"title":"Rational cohomology of \u0000 \u0000 \u0000 M\u0000 \u0000 4\u0000 ,\u0000 1\u0000 \u0000 \u0000 $mathcal {M}_{4,1}$","authors":"Yiu Man Wong,&nbsp;Angelina Zheng","doi":"10.1002/mana.202400294","DOIUrl":"https://doi.org/10.1002/mana.202400294","url":null,"abstract":"<p>We compute the rational cohomology of the moduli space <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathcal {M}_{4,1}$</annotation>\u0000 </semantics></math> of nonsingular genus 4 curves with one marked point, using Gorinov–Vassiliev's method.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1041-1061"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400294","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595435","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
Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elements 拟*-代数中作为特征向量的半线性形式,及其在阶梯元上的应用
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-12 DOI: 10.1002/mana.202400291
Fabio Bagarello, Hiroshi Inoue, Salvatore Triolo
{"title":"Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elements","authors":"Fabio Bagarello,&nbsp;Hiroshi Inoue,&nbsp;Salvatore Triolo","doi":"10.1002/mana.202400291","DOIUrl":"https://doi.org/10.1002/mana.202400291","url":null,"abstract":"<p>We consider a particular class of sesquilinear forms on a Banach quasi *-algebra <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>A</mi>\u0000 <mo>[</mo>\u0000 <mo>∥</mo>\u0000 <mo>.</mo>\u0000 <mo>∥</mo>\u0000 <mo>]</mo>\u0000 <mo>,</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <msub>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mo>∥</mo>\u0000 <mo>.</mo>\u0000 <mo>∥</mo>\u0000 </mrow>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>]</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$({cal A}[Vert .Vert],{cal A}_0[Vert .Vert _0])$</annotation>\u0000 </semantics></math> that we call <i>eigenstates of an element</i> <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 <mo>∈</mo>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$ain {cal A}$</annotation>\u0000 </semantics></math>, and we deduce some of their properties. We further apply our definition to a family of ladder elements, that is, elements of <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>${cal A}$</annotation>\u0000 </semantics></math> obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via Gelfand–Naimark–Segal (GNS) representation.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1062-1075"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400291","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595341","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
Partial Hölder regularity for asymptotically convex functionals with borderline double-phase growth 具有边界双相增长的渐近凸泛函的部分Hölder正则性
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-12 DOI: 10.1002/mana.202400388
Wenrui Chang, Shenzhou Zheng
{"title":"Partial Hölder regularity for asymptotically convex functionals with borderline double-phase growth","authors":"Wenrui Chang,&nbsp;Shenzhou Zheng","doi":"10.1002/mana.202400388","DOIUrl":"https://doi.org/10.1002/mana.202400388","url":null,"abstract":"<p>We study partial Hölder regularity of the local minimizers <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>∈</mo>\u0000 <msubsup>\u0000 <mi>W</mi>\u0000 <mi>loc</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>;</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$uin W_{mathrm{loc}}^{1,1}(Omega;{mathbb {R}^N})$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$Nge 1$</annotation>\u0000 </semantics></math> to the integral functional <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>∫</mo>\u0000 <mi>Ω</mi>\u0000 </msub>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>D</mi>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mspace></mspace>\u0000 <mi>d</mi>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <annotation>$int _Omega F(x,u,Du),dx$</annotation>\u0000 </semantics></math> in a bounded domain <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Omega subset mathbb {R}^n$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$nge 2$</annotation>\u0000 </semantics></math>. Under the assumption of asymptotically convex to the borderline double-phase functional\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1018-1040"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595338","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
A sufficient condition for boundedness of maximal operator on weighted generalized Orlicz spaces 加权广义Orlicz空间上极大算子有界性的充分条件
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-12 DOI: 10.1002/mana.202400496
Vertti Hietanen
{"title":"A sufficient condition for boundedness of maximal operator on weighted generalized Orlicz spaces","authors":"Vertti Hietanen","doi":"10.1002/mana.202400496","DOIUrl":"https://doi.org/10.1002/mana.202400496","url":null,"abstract":"<p>We prove that the Hardy–Littlewood maximal operator is bounded in the weighted generalized Orlicz space if the weight satisfies the classical Muckenhoupt condition <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$A_p$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>→</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>φ</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <msup>\u0000 <mi>t</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$t rightarrow frac{varphi (x,t)}{t^p}$</annotation>\u0000 </semantics></math> is almost increasing in addition to the standard conditions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"944-954"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595434","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
On linearization and uniqueness of preduals 关于前等式的线性化和唯一性
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-12 DOI: 10.1002/mana.202400355
Karsten Kruse
{"title":"On linearization and uniqueness of preduals","authors":"Karsten Kruse","doi":"10.1002/mana.202400355","DOIUrl":"https://doi.org/10.1002/mana.202400355","url":null,"abstract":"&lt;p&gt;We study strong linearizations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar-valued functions. Strong linearizations are special preduals. A locally convex Hausdorff space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {F}(Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of scalar-valued functions on a nonempty set &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;annotation&gt;$Omega$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is said to admit a &lt;i&gt;strong linearization&lt;/i&gt; if there are a locally convex Hausdorff space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;annotation&gt;$Y$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, a map &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$delta: Omega rightarrow Y$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and a topological isomorphism &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;F&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$T: mathcal {F}(Omega)rightarrow Y_{b}^{prime }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &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;f&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∘&lt;/mo&gt;\u0000 &lt;mi&gt;δ&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;$T(f)circ delta = f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for all &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$fin mathcal {F}(Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We give sufficient conditions that allow us to lift strong lin","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"955-975"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400355","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595339","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
On the spaces dual to combinatorial Banach spaces 对偶到组合巴拿赫空间的空间
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-12 DOI: 10.1002/mana.202300303
Piotr Borodulin-Nadzieja, Sebastian Jachimek, Anna Pelczar-Barwacz
{"title":"On the spaces dual to combinatorial Banach spaces","authors":"Piotr Borodulin-Nadzieja,&nbsp;Sebastian Jachimek,&nbsp;Anna Pelczar-Barwacz","doi":"10.1002/mana.202300303","DOIUrl":"https://doi.org/10.1002/mana.202300303","url":null,"abstract":"<p>We present quasi-Banach spaces which are closely related to the duals of combinatorial Banach spaces. More precisely, for a compact family <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math> of finite subsets of <span></span><math>\u0000 <semantics>\u0000 <mi>ω</mi>\u0000 <annotation>$omega$</annotation>\u0000 </semantics></math> we define a quasi-norm <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>∥</mo>\u0000 <mo>·</mo>\u0000 <mo>∥</mo>\u0000 </mrow>\u0000 <mi>F</mi>\u0000 </msup>\u0000 <annotation>$Vert cdot Vert ^mathcal {F}$</annotation>\u0000 </semantics></math> whose Banach envelope is the dual norm for the combinatorial space generated by <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math>. Such quasi-norms seem to be much easier to handle than the dual norms and yet the quasi-Banach spaces induced by them share many properties with the dual spaces. We show that the quasi-Banach spaces induced by large families (in the sense of Lopez-Abad and Todorcevic) are <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$ell _1$</annotation>\u0000 </semantics></math>-saturated and do not have the Schur property. In particular, this holds for the Schreier families.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"998-1017"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595340","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
Weighted Bourgain–Morrey-Besov–Triebel–Lizorkin spaces associated with operators 与算子相关的加权bourgain - morrey - besov - triiebel - lizorkin空间
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-06 DOI: 10.1002/mana.202400223
Tengfei Bai, Jingshi Xu
{"title":"Weighted Bourgain–Morrey-Besov–Triebel–Lizorkin spaces associated with operators","authors":"Tengfei Bai,&nbsp;Jingshi Xu","doi":"10.1002/mana.202400223","DOIUrl":"https://doi.org/10.1002/mana.202400223","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> be a space of homogeneous type and <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> be a nonnegative self-adjoint operator on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^2(X)$</annotation>\u0000 </semantics></math> satisfying a Gaussian upper bound on its heat kernel. First, we obtain the boundedness of the Hardy–Littlewood maximal function and its variant on weighted Bourgain–Morrey spaces. The Hardy-type inequality on sequence Bourgain–Morrey spaces are also given. Then, we introduce the weighted homogeneous Bourgain–Morrey Besov spaces and Triebel–Lizorkin spaces associated with the operator <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>. We obtain characterizations of these spaces in terms of Peetre maximal functions, noncompactly supported functional calculus, and heat kernel. Atomic decompositions and molecular decompositions of weighted homogeneous Bourgain–Morrey Besov spaces and Triebel–Lizorkin spaces are also proved. Finally, we apply our results to prove the boundedness of the fractional power of <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> and the spectral multiplier of <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> on Bourgain–Morrey Besov and Triebel–Lizorkin spaces.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"886-924"},"PeriodicalIF":0.8,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594853","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
Simultaneous approximation by neural network operators with applications to Voronovskaja formulas 神经网络算子的同时逼近与Voronovskaja公式的应用
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-06 DOI: 10.1002/mana.202400281
Marco Cantarini, Danilo Costarelli
{"title":"Simultaneous approximation by neural network operators with applications to Voronovskaja formulas","authors":"Marco Cantarini,&nbsp;Danilo Costarelli","doi":"10.1002/mana.202400281","DOIUrl":"https://doi.org/10.1002/mana.202400281","url":null,"abstract":"<p>In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well-known neural network (NN) operators activated by the sigmoidal function. Other than a uniform convergence theorem for the derivatives of NN operators, we also provide a quantitative estimate for the order of approximation based on the modulus of continuity of the approximated derivative. Furthermore, a qualitative and quantitative Voronovskaja-type formula is established, which provides information about the high order of approximation that can be achieved by NN operators. To prove the above theorems, several auxiliary results involving sigmoidal functions have been established. At the end of the paper, noteworthy examples have been discussed in detail.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"871-885"},"PeriodicalIF":0.8,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400281","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595082","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
L p $L^p$ -boundedness properties for some harmonic analysis operators defined by resolvents for a Laplacian with drift in Euclidean spaces 欧几里德空间中具有漂移的拉普拉斯算子的解所定义的调和分析算子的L p$ L^p$有界性
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2025-02-06 DOI: 10.1002/mana.202400212
Jorge J. Betancor, Juan C. Fariña, Lourdes Rodríguez-Mesa
{"title":"L\u0000 p\u0000 \u0000 $L^p$\u0000 -boundedness properties for some harmonic analysis operators defined by resolvents for a Laplacian with drift in Euclidean spaces","authors":"Jorge J. Betancor,&nbsp;Juan C. Fariña,&nbsp;Lourdes Rodríguez-Mesa","doi":"10.1002/mana.202400212","DOIUrl":"https://doi.org/10.1002/mana.202400212","url":null,"abstract":"&lt;p&gt;We consider the Laplacian with drift in &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; defined by &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;Δ&lt;/mi&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mo&gt;∑&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Delta _nu = sum _{i=1}^n(frac{partial ^2}{partial x_i^2} + 2 nu _ifrac{partial }{partial {x_i}})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;∈&lt;/mo&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;mo&gt;∖&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"849-870"},"PeriodicalIF":0.8,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594855","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
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信