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Mixed weak type inequalities for the fractional maximal operator 分数极大算子的混合弱型不等式
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4354
María Lorente, Francisco J. Martín-Reyes
{"title":"Mixed weak type inequalities for the fractional maximal operator","authors":"María Lorente, Francisco J. Martín-Reyes","doi":"10.33044/revuma.4354","DOIUrl":"https://doi.org/10.33044/revuma.4354","url":null,"abstract":". Let 0 ≤ α < n , q = nn − α . We establish the mixed weak type inequality sup λ> 0 λ q Z { x ∈ R n : M α f ( x ) >λv ( x ) }","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136153588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Boundedness of fractional operators associated with Schrödinger operators on weighted variable Lebesgue spaces via extrapolation 外推加权变量Lebesgue空间上Schrödinger算子相关分数算子的有界性
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4347
Rocío Ayala, Adrian Cabral
{"title":"Boundedness of fractional operators associated with Schrödinger operators on weighted variable Lebesgue spaces via extrapolation","authors":"Rocío Ayala, Adrian Cabral","doi":"10.33044/revuma.4347","DOIUrl":"https://doi.org/10.33044/revuma.4347","url":null,"abstract":"In this work we obtain boundedness results for fractional operators associated with Schr\"odinger operators $ mathcal{L}=-Delta+V$ on weighted variable Lebesgue spaces. These operators include fractional integrals and their respective commutators. Particularly, we obtain weighted inequalities of the type $L^{p(cdot)}$-$L^{q(cdot)}$ and estimates of the type $L^{p(cdot)}$-Lipschitz variable integral spaces. For this purpose, we developed extrapolation results that allow us to obtain boundedness results of the type described above in the variable setting by starting from analogous inequalities in the classical context.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
$L^p(mathbb{R}^n)$-dimension free estimates of the Riesz transforms $L^p(mathbb{R}^n)$-维Riesz变换的自由估计
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4359
José L. Torrea
{"title":"$L^p(mathbb{R}^n)$-dimension free estimates of the Riesz transforms","authors":"José L. Torrea","doi":"10.33044/revuma.4359","DOIUrl":"https://doi.org/10.33044/revuma.4359","url":null,"abstract":"","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136153584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 fractional operators with more than one singularity 关于具有一个以上奇点的分数算子
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4364
María Silvina Riveros, Raúl E. Vidal
{"title":"On fractional operators with more than one singularity","authors":"María Silvina Riveros, Raúl E. Vidal","doi":"10.33044/revuma.4364","DOIUrl":"https://doi.org/10.33044/revuma.4364","url":null,"abstract":". Let 0 ≤ α < n , m ∈ N and let T α,m be an integral operator given by a kernel of the form K ( x,y ) = k 1 ( x − A 1 y ) k 2 ( x − A 2 y ) ...k m ( x − A m y ) , where A i are invertible matrices and each k i satisfies a fractional size and a generalized fractional H¨ormander condition that depends on α . In this survey, written in honour to Eleonor Harboure, we collect several results about boundedness in different spaces of the operator T α,m , obtained along the last 35 years by several members of the Analysis Group of FAMAF, UNC.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Avatars of Stein's theorem in the complex setting 复杂环境下斯坦定理的化身
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4361
Aline Bonami, Sandrine Grellier, Benoît Sehba
{"title":"Avatars of Stein's theorem in the complex setting","authors":"Aline Bonami, Sandrine Grellier, Benoît Sehba","doi":"10.33044/revuma.4361","DOIUrl":"https://doi.org/10.33044/revuma.4361","url":null,"abstract":". In this paper, we establish some variants of Stein’s theorem, which states that a non-negative function belongs to the Hardy space H 1 ( T ) if and only if it belongs to L log L ( T ). We consider Bergman spaces of holomorphic functions in the upper half plane and develop avatars of Stein’s theorem and relative results in this context. We are led to consider weighted Bergman spaces and Bergman spaces of Musielak–Orlicz type. Eventually, we characterize bounded Hankel operators on A 1 ( C + ).","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136152901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Learning the model from the data 从数据中学习模型
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4371
Carlos Cabrelli, Ursula Molter
{"title":"Learning the model from the data","authors":"Carlos Cabrelli, Ursula Molter","doi":"10.33044/revuma.4371","DOIUrl":"https://doi.org/10.33044/revuma.4371","url":null,"abstract":". The task of approximating data with a concise model comprising only a few parameters is a key concern in many applications, particularly in signal processing. These models, typically subspaces belonging to a specific class, are carefully chosen based on the data at hand. In this survey, we review the latest research on data approximation using models with few parameters, with a specific emphasis on scenarios where the data is situated in finite-dimensional vector spaces, functional spaces such as L 2 ( R d ), and other general situations. We highlight the invariant properties of these subspace-based models that make them suitable for diverse applications, particularly in the field of image processing.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136153378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Segal–Bargmann transforms and holomorphic Sobolev spaces of fractional order 分数阶的Segal-Bargmann变换与全纯Sobolev空间
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4363
Sundaram Thangavelu
{"title":"Segal–Bargmann transforms and holomorphic Sobolev spaces of fractional order","authors":"Sundaram Thangavelu","doi":"10.33044/revuma.4363","DOIUrl":"https://doi.org/10.33044/revuma.4363","url":null,"abstract":". In this note we investigate the image of Sobolev spaces of fractional order on a compact Lie group K under the Segal–Bargmann transform. We show that the image can be characterised in terms of certain weighted Bergman spaces of holomorphic functions on the complexification extending a theorem of Hall and Lewkeeratiyutkul. We also treat the heat kernel transform associated to the Hermite operator.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Hermite Besov and Triebel–Lizorkin spaces and applications Hermite Besov和triiebel - lizorkin空间及其应用
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4360
Fu Ken Ly, Virginia Naibo
{"title":"Hermite Besov and Triebel–Lizorkin spaces and applications","authors":"Fu Ken Ly, Virginia Naibo","doi":"10.33044/revuma.4360","DOIUrl":"https://doi.org/10.33044/revuma.4360","url":null,"abstract":". We present an overview of Besov and Triebel–Lizorkin spaces in the Hermite setting and applications on boundedness properties of Hermite pseudo-multipliers and fractional Leibniz rules in such spaces. We also give a new weighted estimate for Hermite multipliers for weights related to Hermite operators.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Extrapolation of compactness for certain pseudodifferential operators 一类伪微分算子紧性的外推
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4365
María J. Carro, Javier Soria, Rodolfo H. Torres
{"title":"Extrapolation of compactness for certain pseudodifferential operators","authors":"María J. Carro, Javier Soria, Rodolfo H. Torres","doi":"10.33044/revuma.4365","DOIUrl":"https://doi.org/10.33044/revuma.4365","url":null,"abstract":". A recently developed extrapolation of compactness on weighted Lebesgue spaces is revisited and a new application to a class of compact pseu-dodifferential operators is presented.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Upper endpoint estimates and extrapolation for commutators 换向子的上端点估计和外推
4区 数学
Revista De La Union Matematica Argentina Pub Date : 2023-09-21 DOI: 10.33044/revuma.4362
Kangwei Li, Sheldy Ombrosi, Israel P. Rivera-Ríos
{"title":"Upper endpoint estimates and extrapolation for commutators","authors":"Kangwei Li, Sheldy Ombrosi, Israel P. Rivera-Ríos","doi":"10.33044/revuma.4362","DOIUrl":"https://doi.org/10.33044/revuma.4362","url":null,"abstract":"In this note we revisit the upper endpoint estimates for commutators following the line by Harboure, Segovia and Torrea. Relying upon the suitable BMO subspace suited for the commutator that was introduced by Accomazzo, we obtain a counterpart for commutators of the upper endpoint extrapolation result by Harboure, Mac'ias and Segovia. Multilinear counterparts are provided as well.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136236231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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