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Banach–Stone theorems for disjointness preserving relations 不相交保全关系的巴拿赫-斯通定理
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-02-29 DOI: 10.1007/s43037-024-00327-z
Denny H. Leung, Wee Kee Tang
{"title":"Banach–Stone theorems for disjointness preserving relations","authors":"Denny H. Leung, Wee Kee Tang","doi":"10.1007/s43037-024-00327-z","DOIUrl":"https://doi.org/10.1007/s43037-024-00327-z","url":null,"abstract":"<p>The concept of disjointness preserving mappings has proved to be a useful unifying idea in the study of Banach–Stone type theorems. In this paper, we examine disjointness preserving relations between sets of continuous functions (valued in general topological spaces). Under very mild assumptions, it is shown that a disjointness preserving relation is completely determined by a Boolean isomorphism between the Boolean algebras of regular open sets in the domain spaces. Building on this result, certain Banach–Stone type theorems are obtained for disjointness preserving relations. From these, we deduce a generalization of Kaplansky’s classical theorem concerning order isomorphisms to sets of continuous functions with values topological lattices. As another application, we prove some results on the characterization of nonvanishing preservers. Throughout, the domains of the function spaces need not be compact.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Sharp embedding between Wiener amalgam and some classical spaces 维纳汞齐与某些经典空间之间的锐嵌入
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-02-29 DOI: 10.1007/s43037-023-00323-9
{"title":"Sharp embedding between Wiener amalgam and some classical spaces","authors":"","doi":"10.1007/s43037-023-00323-9","DOIUrl":"https://doi.org/10.1007/s43037-023-00323-9","url":null,"abstract":"<h3>Abstract</h3> <p>This paper investigates the embedding relationships between Wiener amalgam spaces and classical spaces, including Sobolev spaces, local Hardy spaces, Besov spaces, and <span> <span>(alpha )</span> </span>-modulation spaces. By establishing exact conditions, we provide a detailed characterization of the embeddings between Wiener amalgam spaces and these classical spaces, particularly the most general case when <span> <span>(alpha =0)</span> </span>, which extend the main results obtained by Guo–Wu–Yang–Zhao (J Funct Anal 273(1):404–443, 2017). Furthermore, we discuss the embedding relationship between Wiener amalgam spaces and Triebel–Lizorkin spaces <span> <span>(F_{p,r}^{s})</span> </span> when <span> <span>(0&lt;pleqslant 1)</span> </span>.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Commutators for certain fractional type operators on weighted spaces and Orlicz–Morrey spaces 加权空间和奥利兹-莫雷空间上某些分数型算子的换元器
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-02-28 DOI: 10.1007/s43037-024-00325-1
{"title":"Commutators for certain fractional type operators on weighted spaces and Orlicz–Morrey spaces","authors":"","doi":"10.1007/s43037-024-00325-1","DOIUrl":"https://doi.org/10.1007/s43037-024-00325-1","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we focus on a class of fractional type integral operators that can be served as extensions of Riesz potential with kernels <span> <span>$$begin{aligned} K(x,y)=frac{Omega _1(x-A_1 y)}{|x-A_1 y |^{{n}/{q_1}}} cdots frac{Omega _m(x-A_m y)}{|x-A_m y |^{{n}/{q_m}}}, end{aligned}$$</span> </span>where <span> <span>(alpha in [0,n))</span> </span>, <span> <span>( mgeqslant 1)</span> </span>, <span> <span>(sum limits _{i=1}^mfrac{n}{q_i}=n-alpha )</span> </span>, <span> <span>({A_i}^m_{i=1})</span> </span> are invertible matrixes, <span> <span>(Omega _i)</span> </span> is homogeneous of degree 0 on <span> <span>(mathbb R^n)</span> </span> and <span> <span>(Omega _iin L^{p_i}(S^{n-1}))</span> </span> for some <span> <span>(p_iin [1,infty ))</span> </span>. Under appropriate assumptions, we obtain the weighted <span> <span>(L^p(mathbb R^n)-L^q(mathbb R^n))</span> </span> estimates as well as weighted <span> <span>(H^p(mathbb R^n)-L^q(mathbb R^n))</span> </span> estimates of the commutators for such operators with <em>BMO</em>-type function when <span> <span>(frac{1}{q}=frac{1}{p}-frac{alpha }{n})</span> </span>. In addition, we acquire the boundedness of these operators and their commutators with a function in Campanato spaces on Orcliz–Morrey spaces as well as the compactness for such commutators in a special case: <span> <span>(m=1)</span> </span> and <span> <span>(A=I)</span> </span>.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"44 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Non-smooth atomic decomposition of Triebel–Lizorkin-type spaces Triebel-Lizorkin 型空间的非光滑原子分解
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-02-22 DOI: 10.1007/s43037-023-00321-x
Yoshihiro Sawano, Dachun Yang, Wen Yuan
{"title":"Non-smooth atomic decomposition of Triebel–Lizorkin-type spaces","authors":"Yoshihiro Sawano, Dachun Yang, Wen Yuan","doi":"10.1007/s43037-023-00321-x","DOIUrl":"https://doi.org/10.1007/s43037-023-00321-x","url":null,"abstract":"<p>In this article, the authors establish a non-smooth atomic decomposition of Triebel–Lizorkin-type spaces and, as a by-product, a non-smooth atomic decomposition of subspaces of BMO spaces is obtained. An application of this decomposition method to the boundedness of Marcinkiewicz integral operators is also presented.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"3 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139947556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Greedy-like bases for sequences with gaps 有间隙序列的类贪心碱基
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-02-21 DOI: 10.1007/s43037-024-00324-2
Miguel Berasategui, Pablo M. Berná
{"title":"Greedy-like bases for sequences with gaps","authors":"Miguel Berasategui, Pablo M. Berná","doi":"10.1007/s43037-024-00324-2","DOIUrl":"https://doi.org/10.1007/s43037-024-00324-2","url":null,"abstract":"<p>In 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the <span>({{textbf {n}}})</span>-<i>t</i>-quasi-greedy property that is based on them. Building upon this foundation, our current work aims to further investigate these algorithms and bases while introducing new ideas for two primary purposes. First, we aim to prove that for <span>({{textbf {n}}})</span> with bounded quotient gaps, <span>({{textbf {n}}})</span>-<i>t</i>-quasi-greedy bases are quasi-greedy bases. This generalization extends a previous result to the context of Markushevich bases and, also, completes the answer to a question by Oikhberg. The second objective is to extend certain approximation properties of the greedy algorithm to the context of sequences with gaps and study if there is a relationship between this new extension and the usual convergence.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"37 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Limiting dynamics for stochastic delay p-Laplacian equation on unbounded thin domains 无界薄域上随机延迟 p-Laplacian 方程的极限动力学
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-02-18 DOI: 10.1007/s43037-024-00326-0
Fuzhi Li, Dingshi Li, Mirelson M. Freitas
{"title":"Limiting dynamics for stochastic delay p-Laplacian equation on unbounded thin domains","authors":"Fuzhi Li, Dingshi Li, Mirelson M. Freitas","doi":"10.1007/s43037-024-00326-0","DOIUrl":"https://doi.org/10.1007/s43037-024-00326-0","url":null,"abstract":"<p>We study the long-term behavior of solutions for stochastic delay <i>p</i>-Laplacian equation with multiplicative noise on unbounded thin domains. We first prove the existence and uniqueness of tempered random attractors for these equations defined on <span>((n+1))</span>-dimensional unbounded thin domains. Then, the upper semicontinuity of these attractors when a family of <span>((n+1))</span>-dimensional thin domains degenerates onto an <i>n</i>-dimensional domain as the thinness measure approaches zero is established.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"51 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139904003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 solvability of inhomogeneous boundary-value problems in Sobolev spaces 索波列夫空间中不均匀边界值问题的可解性
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-02-17 DOI: 10.1007/s43037-023-00316-8
Vladimir Mikhailets, Olena Atlasiuk
{"title":"The solvability of inhomogeneous boundary-value problems in Sobolev spaces","authors":"Vladimir Mikhailets, Olena Atlasiuk","doi":"10.1007/s43037-023-00316-8","DOIUrl":"https://doi.org/10.1007/s43037-023-00316-8","url":null,"abstract":"<p>The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be overdetermined or underdetermined. They may contain derivatives, of the unknown vector-valued function, whose integer or fractional orders exceed the order of the differential equation. Similar problems arise naturally in various applications. The theory introduces the notion of a rectangular number characteristic matrix of the problem. The index and Fredholm numbers of this matrix coincide, respectively, with the index and Fredholm numbers of the inhomogeneous boundary-value problem. Unlike the index, the Fredholm numbers (i.e., the dimensions of the problem kernel and co-kernel) are unstable even with respect to small (in the norm) finite-dimensional perturbations. We give examples in which the characteristic matrix can be explicitly found. We also prove a limit theorem for a sequence of characteristic matrices. Specifically, it follows from this theorem that the Fredholm numbers of the problems under investigation are semicontinuous in the strong operator topology. Such a property ceases to be valid in the general case.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"41 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Characterizations of generalized pencils of pairs of projections 投影对的广义铅笔的特征
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-02-12 DOI: 10.1007/s43037-023-00322-w
Tao Chen, Weining Lai, Chunyuan Deng
{"title":"Characterizations of generalized pencils of pairs of projections","authors":"Tao Chen, Weining Lai, Chunyuan Deng","doi":"10.1007/s43037-023-00322-w","DOIUrl":"https://doi.org/10.1007/s43037-023-00322-w","url":null,"abstract":"<p>Let <i>T</i> be a bounded linear operator on a complex Hilbert space <span>(mathcal {H})</span>. We present some necessary and sufficient conditions for <i>T</i> to be the generalized pencil <span>(P + alpha Q +beta PQ)</span> of a pair (<i>P</i>, <i>Q</i>) of projections at some point <span>((alpha , beta )in mathbb {C}^2)</span>. The range and kernel relations of the generalized pencil <i>T</i> are studied and comments on the additional properties of some special generalized pencil are given.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"16 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Sharp norm estimates for functional dual affine quermassintegrals 函数对偶仿射质积分的锐规范估计
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-01-28 DOI: 10.1007/s43037-023-00319-5
Songjun Lv
{"title":"Sharp norm estimates for functional dual affine quermassintegrals","authors":"Songjun Lv","doi":"10.1007/s43037-023-00319-5","DOIUrl":"https://doi.org/10.1007/s43037-023-00319-5","url":null,"abstract":"<p>This paper presents refined estimates for functional dual affine quermassintegrals, building upon the estimates of Dann et al. To sharpen the inequality, Dann et al. (Proc. Lond. Math. Soc. (3) 113(2):140–162, 2016) incorporated an <span>(L^infty)</span>-weight into the integration. We further refine these estimates and extend the <span>(L^infty)</span>-weight estimates to include a wider range of <span>(L^{lambda })</span>-weights where <span>(lambda &gt;1.)</span></p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"325 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
p-Summing Bloch mappings on the complex unit disc 复杂单位圆盘上的p求和布洛赫映射
IF 1.2 2区 数学
Banach Journal of Mathematical Analysis Pub Date : 2024-01-22 DOI: 10.1007/s43037-023-00318-6
M. G. Cabrera-Padilla, A. Jiménez-Vargas, D. Ruiz-Casternado
{"title":"p-Summing Bloch mappings on the complex unit disc","authors":"M. G. Cabrera-Padilla, A. Jiménez-Vargas, D. Ruiz-Casternado","doi":"10.1007/s43037-023-00318-6","DOIUrl":"https://doi.org/10.1007/s43037-023-00318-6","url":null,"abstract":"<p>The notion of <i>p</i>-summing Bloch mapping from the complex unit open disc <span>(mathbb {D})</span> into a complex Banach space <i>X</i> is introduced for any <span>(1le ple infty .)</span> It is shown that the linear space of such mappings, equipped with a natural seminorm <span>(pi ^{mathcal {B}}_p,)</span> is Möbius-invariant. Moreover, its subspace consisting of all those mappings which preserve the zero is an injective Banach ideal of normalized Bloch mappings. Bloch versions of the Pietsch’s domination/factorization Theorem and the Maurey’s extrapolation Theorem are presented. We also introduce the spaces of <i>X</i>-valued Bloch molecules on <span>(mathbb {D})</span> and identify the spaces of normalized <i>p</i>-summing Bloch mappings from <span>(mathbb {D})</span> into <span>(X^*)</span> under the norm <span>(pi ^{mathcal {B}}_p)</span> with the duals of such spaces of molecules under the Bloch version of the <span>(p^*)</span>-Chevet–Saphar tensor norms <span>(d_{p^*}.)</span></p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"19 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139553403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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