Pub Date : 2023-09-15DOI: 10.1007/s00041-023-10040-4
Pamela A. Muller, Israel P. Rivera-Ríos
Abstract In this paper endpoint entropy Fefferman–Stein bounds for Calderón–Zygmund operators introduced by Rahm (J Math Anal Appl 504(1):Paper No. 125372, 2021) are extended to iterated Coifman–Rochberg–Weiss commutators.
本文将Rahm引入的Calderón-Zygmund算子的端点熵Fefferman-Stein界(J Math Anal applied 504(1): paper No. 125372, 2021)推广到迭代Coifman-Rochberg-Weiss换向子。
{"title":"Endpoint Entropy Fefferman–Stein Bounds for Commutators","authors":"Pamela A. Muller, Israel P. Rivera-Ríos","doi":"10.1007/s00041-023-10040-4","DOIUrl":"https://doi.org/10.1007/s00041-023-10040-4","url":null,"abstract":"Abstract In this paper endpoint entropy Fefferman–Stein bounds for Calderón–Zygmund operators introduced by Rahm (J Math Anal Appl 504(1):Paper No. 125372, 2021) are extended to iterated Coifman–Rochberg–Weiss commutators.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135394387","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}
Pub Date : 2023-09-12DOI: 10.1007/s00041-023-10035-1
Oleh Lopushansky
Abstract Estimates of best approximations by exponential type analytic functions in Gaussian random variables with respect to the Malliavin derivative in the form of Bernstein–Jackson inequalities with exact constants are established. Formulas for constants are expressed through basic parameters of approximation spaces. The relationship between approximation Gaussian Hilbert spaces and classic Besov spaces are shown.
{"title":"Bernstein–Jackson Inequalities on Gaussian Hilbert Spaces","authors":"Oleh Lopushansky","doi":"10.1007/s00041-023-10035-1","DOIUrl":"https://doi.org/10.1007/s00041-023-10035-1","url":null,"abstract":"Abstract Estimates of best approximations by exponential type analytic functions in Gaussian random variables with respect to the Malliavin derivative in the form of Bernstein–Jackson inequalities with exact constants are established. Formulas for constants are expressed through basic parameters of approximation spaces. The relationship between approximation Gaussian Hilbert spaces and classic Besov spaces are shown.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135878108","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}
Pub Date : 2023-08-22DOI: 10.1007/s00041-023-10038-y
Linhao Song, Jun Fan, Diao Chen, Ding-Xuan Zhou
{"title":"Correction: Approximation of Nonlinear Functionals Using Deep ReLU Networks","authors":"Linhao Song, Jun Fan, Diao Chen, Ding-Xuan Zhou","doi":"10.1007/s00041-023-10038-y","DOIUrl":"https://doi.org/10.1007/s00041-023-10038-y","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48684535","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}
Pub Date : 2023-08-17DOI: 10.1007/s00041-023-10033-3
Alexandre Almeida, H. Rafeiro
{"title":"Correction: Maximal Operator in Variable Stummel Spaces","authors":"Alexandre Almeida, H. Rafeiro","doi":"10.1007/s00041-023-10033-3","DOIUrl":"https://doi.org/10.1007/s00041-023-10033-3","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49617381","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}
Pub Date : 2023-08-01DOI: 10.1007/s00041-023-10026-2
David Bartusel
Abstract We study the phase retrieval problem for the short-time Fourier transform on the groups $${mathbb {Z}}$$ Z , $${mathbb {Z}}_d$$ Zd and $${{mathbb {R}}}^d$$ Rd . As is well-known, phase retrieval is possible once the windows’s ambiguity function vanishes nowhere. However, there are only few results for windows that fail to meet this condition. The goal of this paper is to establish new and complete characterizations for phase retrieval with more general windows and compare them to existing results. For a fixed window, our uniqueness conditions usually only depend on the signal’s support and are therefore easily comprehensible. In the discrete settings, we also provide examples which show that a non-vanishing ambiguity function is not necessary for a window to do phase retrieval.
摘要研究了$${mathbb {Z}}$$ Z、$${mathbb {Z}}_d$$ Z d和$${{mathbb {R}}}^d$$ R d群上短时傅里叶变换的相位恢复问题。众所周知，一旦窗口的模糊函数消失，相位恢复是可能的。然而，对于不满足此条件的窗口，只有少数结果。本文的目标是用更一般的窗口建立新的和完整的相位检索表征，并将它们与现有的结果进行比较。对于一个固定的窗口，我们的唯一性条件通常只依赖于信号的支持，因此很容易理解。在离散设置中，我们还提供了一些例子，表明非消失模糊函数对于窗口进行相位检索是不必要的。
{"title":"Injectivity Conditions for STFT Phase Retrieval on $${mathbb {Z}}$$, $${mathbb {Z}}_d$$ and $${{mathbb {R}}}^d$$","authors":"David Bartusel","doi":"10.1007/s00041-023-10026-2","DOIUrl":"https://doi.org/10.1007/s00041-023-10026-2","url":null,"abstract":"Abstract We study the phase retrieval problem for the short-time Fourier transform on the groups $${mathbb {Z}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Z</mml:mi> </mml:math> , $${mathbb {Z}}_d$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> and $${{mathbb {R}}}^d$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:math> . As is well-known, phase retrieval is possible once the windows’s ambiguity function vanishes nowhere. However, there are only few results for windows that fail to meet this condition. The goal of this paper is to establish new and complete characterizations for phase retrieval with more general windows and compare them to existing results. For a fixed window, our uniqueness conditions usually only depend on the signal’s support and are therefore easily comprehensible. In the discrete settings, we also provide examples which show that a non-vanishing ambiguity function is not necessary for a window to do phase retrieval.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136106825","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}
Pub Date : 2023-07-28DOI: 10.1007/s00041-023-10032-4
T. A. Bui, X. Duong
{"title":"New Atomic Decomposition for Besov Type Space B˙1,10documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$dot{B}^0_{1,1}$$","authors":"T. A. Bui, X. Duong","doi":"10.1007/s00041-023-10032-4","DOIUrl":"https://doi.org/10.1007/s00041-023-10032-4","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42728668","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}
Pub Date : 2023-07-08DOI: 10.1007/s00041-023-10023-5
M. Hirn, A. Little
{"title":"Power Spectrum Unbiasing for Dilation-Invariant Multi-reference Alignment","authors":"M. Hirn, A. Little","doi":"10.1007/s00041-023-10023-5","DOIUrl":"https://doi.org/10.1007/s00041-023-10023-5","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44831226","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}
Pub Date : 2023-06-01DOI: 10.1007/s00041-023-10018-2
Wei Wei, Yanqing Wang, Yulin Ye
{"title":"Gagliardo–Nirenberg Inequalities in Lorentz Type Spaces","authors":"Wei Wei, Yanqing Wang, Yulin Ye","doi":"10.1007/s00041-023-10018-2","DOIUrl":"https://doi.org/10.1007/s00041-023-10018-2","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47201251","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}
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