Pub Date : 2023-11-01DOI: 10.1007/s00041-023-10050-2
Bernd Schmidt, Martin Steinbach
Abstract We study structural properties and the harmonic analysis of discrete subgroups of the Euclidean group. In particular, we 1. obtain an efficient description of their dual space, 2. develop Fourier analysis methods for periodic mappings on them, and 3. prove a Schur-Zassenhaus type splitting result.
{"title":"On Discrete Groups of Euclidean Isometries: Representation Theory, Harmonic Analysis and Splitting Properties","authors":"Bernd Schmidt, Martin Steinbach","doi":"10.1007/s00041-023-10050-2","DOIUrl":"https://doi.org/10.1007/s00041-023-10050-2","url":null,"abstract":"Abstract We study structural properties and the harmonic analysis of discrete subgroups of the Euclidean group. In particular, we 1. obtain an efficient description of their dual space, 2. develop Fourier analysis methods for periodic mappings on them, and 3. prove a Schur-Zassenhaus type splitting result.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103227","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 : 2023-10-20DOI: 10.1007/s00041-023-10041-3
Sauli Lindberg
Abstract Coifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator and other compensated compactness quantities map their natural domain of definition onto the real-variable Hardy space $$mathcal {H}^1({mathbb {R}}^n)$$ H1(Rn) . We present an axiomatic, Banach space geometric approach to the problem in the case of quadratic operators. We also make progress on the main open case, the Jacobian equation in the plane.
{"title":"A Note on the Jacobian Problem of Coifman, Lions, Meyer and Semmes","authors":"Sauli Lindberg","doi":"10.1007/s00041-023-10041-3","DOIUrl":"https://doi.org/10.1007/s00041-023-10041-3","url":null,"abstract":"Abstract Coifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator and other compensated compactness quantities map their natural domain of definition onto the real-variable Hardy space $$mathcal {H}^1({mathbb {R}}^n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . We present an axiomatic, Banach space geometric approach to the problem in the case of quadratic operators. We also make progress on the main open case, the Jacobian equation in the plane.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135567843","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 : 2023-10-17DOI: 10.1007/s00041-023-10043-1
Suddhasattwa Das, Dimitrios Giannakis, Michael R. Montgomery
{"title":"Correction to: On Harmonic Hilbert Spaces on Compact Abelian Groups","authors":"Suddhasattwa Das, Dimitrios Giannakis, Michael R. Montgomery","doi":"10.1007/s00041-023-10043-1","DOIUrl":"https://doi.org/10.1007/s00041-023-10043-1","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135993911","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 : 2023-10-17DOI: 10.1007/s00041-023-10048-w
F. Colombo, S. Pinton, I. Sabadini, D. C. Struppa
Abstract In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential operators whose symbol is a function that is holomorphic in some open set, but not necessarily entire. The results proved for superoscillating sequences in several variables are extended to sequences of supershifts in several variables.
{"title":"The General Theory of Superoscillations and Supershifts in Several Variables","authors":"F. Colombo, S. Pinton, I. Sabadini, D. C. Struppa","doi":"10.1007/s00041-023-10048-w","DOIUrl":"https://doi.org/10.1007/s00041-023-10048-w","url":null,"abstract":"Abstract In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential operators whose symbol is a function that is holomorphic in some open set, but not necessarily entire. The results proved for superoscillating sequences in several variables are extended to sequences of supershifts in several variables.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994637","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 : 2023-10-01DOI: 10.1007/s00041-023-10045-z
Michael Baake, Timo Spindeler, Nicolae Strungaru
Abstract Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on $$mathbb {R}hspace{0.5pt}^d$$ Rd . In particular, we classify all periodic eigenmeasures on $$mathbb {R}hspace{0.5pt}$$ R , which gives an interesting connection with the discrete Fourier transform and its eigenvectors, as well as all eigenmeasures on $$mathbb {R}hspace{0.5pt}$$ R with uniformly discrete support. An interesting subclass of the latter emerges from the classic cut and project method for aperiodic Meyer sets. Finally, we construct a large class of eigenmeasures with locally finite support that is not uniformly discrete and has large gaps around 0.
摘要:本文描述了几类调质测度，它们是傅里叶变换的特征测度，后者被看作是$$mathbb {R}hspace{0.5pt}^d$$ R d上Radon测度(通常是无界的)的线性算子。特别地，我们对$$mathbb {R}hspace{0.5pt}$$ R上的所有周期特征测度进行了分类，它给出了与离散傅里叶变换及其特征向量的有趣联系，以及具有一致离散支持的$$mathbb {R}hspace{0.5pt}$$ R上的所有特征测度。后者的一个有趣的子类出现在非周期Meyer集的经典切割和投影方法中。最后，我们构造了一大类具有局部有限支持的特征测度，它不是一致离散的，并且在0附近有很大的间隙。
{"title":"On Eigenmeasures Under Fourier Transform","authors":"Michael Baake, Timo Spindeler, Nicolae Strungaru","doi":"10.1007/s00041-023-10045-z","DOIUrl":"https://doi.org/10.1007/s00041-023-10045-z","url":null,"abstract":"Abstract Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on $$mathbb {R}hspace{0.5pt}^d$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>R</mml:mi> <mml:msup> <mml:mspace /> <mml:mi>d</mml:mi> </mml:msup> </mml:mrow> </mml:math> . In particular, we classify all periodic eigenmeasures on $$mathbb {R}hspace{0.5pt}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mspace /> </mml:mrow> </mml:math> , which gives an interesting connection with the discrete Fourier transform and its eigenvectors, as well as all eigenmeasures on $$mathbb {R}hspace{0.5pt}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mspace /> </mml:mrow> </mml:math> with uniformly discrete support. An interesting subclass of the latter emerges from the classic cut and project method for aperiodic Meyer sets. Finally, we construct a large class of eigenmeasures with locally finite support that is not uniformly discrete and has large gaps around 0.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136119560","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 : 2023-10-01DOI: 10.1007/s00041-023-10046-y
Patrick Erik Bradley
Abstract A class of heat operators over non-archimedean local fields acting on $$L_2$$ L2 -function spaces on holed discs in the local field are developed and seen as being operators previously introduced by Zúñiga-Galindo, and if the underlying trees are regular, they are associated here with certain finite Kronecker product graphs. $$L_2$$ L2 -spaces and integral operators invariant under the action of a finite group acting on a holed disc are studied, and then applied to Mumford curves. It is found that the spectral gap in families of Mumford curves can become arbitrarily small.
{"title":"Heat Equations and Wavelets on Mumford Curves and Their Finite Quotients","authors":"Patrick Erik Bradley","doi":"10.1007/s00041-023-10046-y","DOIUrl":"https://doi.org/10.1007/s00041-023-10046-y","url":null,"abstract":"Abstract A class of heat operators over non-archimedean local fields acting on $$L_2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -function spaces on holed discs in the local field are developed and seen as being operators previously introduced by Zúñiga-Galindo, and if the underlying trees are regular, they are associated here with certain finite Kronecker product graphs. $$L_2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -spaces and integral operators invariant under the action of a finite group acting on a holed disc are studied, and then applied to Mumford curves. It is found that the spectral gap in families of Mumford curves can become arbitrarily small.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135407675","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 : 2023-10-01DOI: 10.1007/s00041-023-10044-0
Elizabeth Hale, Virginia Naibo
{"title":"Fractional Leibniz Rules in the Setting of Quasi-Banach Function Spaces","authors":"Elizabeth Hale, Virginia Naibo","doi":"10.1007/s00041-023-10044-0","DOIUrl":"https://doi.org/10.1007/s00041-023-10044-0","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135662905","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 : 2023-10-01DOI: 10.1007/s00041-023-10049-9
Surjeet Singh Choudhary, K. Jotsaroop, Saurabh Shrivastava, Kalachand Shuin
{"title":"Bilinear Bochner–Riesz Square Function and Applications","authors":"Surjeet Singh Choudhary, K. Jotsaroop, Saurabh Shrivastava, Kalachand Shuin","doi":"10.1007/s00041-023-10049-9","DOIUrl":"https://doi.org/10.1007/s00041-023-10049-9","url":null,"abstract":"","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136119573","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 : 2023-09-22DOI: 10.1007/s00041-023-10042-2
Tohru Ozawa, Taiki Takeuchi
Abstract The heat semigroup $${T(t)}_{t ge 0}$$ {T(t)}t≥0 defined on homogeneous Besov spaces $$dot{B}_{p,q}^s(mathbb {R}^n)$$ B˙p,qs(Rn) is considered. We show the decay estimate of $$T(t)f in dot{B}_{p,1}^{s+sigma }(mathbb {R}^n)$$ T(t)f∈B˙p,1s+σ(Rn) for $$f in dot{B}_{p,infty }^s(mathbb {R}^n)$$ f∈B˙p,∞s(Rn) with an explicit bound depending only on the regularity index $$sigma >0$$ σ>0 and space dimension n . It may be regarded as a refined result compared with that of the second author (Takeuchi in Partial Differ Equ Appl Math 4 :100174, 2021). As a result of the refined decay estimate, we also improve a lower bound estimate of the radius of convergence of the Taylor expansion of $$T(cdot )f$$ T(·)f in space and time. To refine the previous results, we show explicit pointwise estimates of higher order derivatives of the power function $$|xi |^{sig
摘要考虑齐次Besov空间$$dot{B}_{p,q}^s(mathbb {R}^n)$$ B˙p, q s {(R n)}上定义的热半群$${T(t)}_{t ge 0}$$ T (T) T≥0。我们给出了$$T(t)f in dot{B}_{p,1}^{s+sigma }(mathbb {R}^n)$$ T (T) f∈B˙p, 1 s + σ (R n)对于$$f in dot{B}_{p,infty }^s(mathbb {R}^n)$$ f∈B˙p，∞s (R n)的衰减估计，其显式界仅依赖于正则性指标$$sigma >0$$ σ ＆gt;0和空间维数n。与第二作者(Takeuchi in Partial Differ Equ, apple Math 4:100174, 2021)的结果相比，可以认为是一个改进的结果。由于改进了衰减估计，我们还改进了$$T(cdot )f$$ T(·)f的泰勒展开在空间和时间上的收敛半径的下界估计。为了完善之前的结果，我们给出了对$$sigma in mathbb {R}$$ σ∈R的幂函数$$|xi |^{sigma }$$ | ξ | σ的高阶导数的显式点估计。此外，我们还改进了热核导数的$$L^1$$ L -估计。
{"title":"Refined Decay Estimate and Analyticity of Solutions to the Linear Heat Equation in Homogeneous Besov Spaces","authors":"Tohru Ozawa, Taiki Takeuchi","doi":"10.1007/s00041-023-10042-2","DOIUrl":"https://doi.org/10.1007/s00041-023-10042-2","url":null,"abstract":"Abstract The heat semigroup $${T(t)}_{t ge 0}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>T</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>}</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> defined on homogeneous Besov spaces $$dot{B}_{p,q}^s(mathbb {R}^n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> is considered. We show the decay estimate of $$T(t)f in dot{B}_{p,1}^{s+sigma }(mathbb {R}^n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>f</mml:mi> <mml:mo>∈</mml:mo> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> <mml:mi>σ</mml:mi> </mml:mrow> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> for $$f in dot{B}_{p,infty }^s(mathbb {R}^n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>∈</mml:mo> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> with an explicit bound depending only on the regularity index $$sigma >0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and space dimension n . It may be regarded as a refined result compared with that of the second author (Takeuchi in Partial Differ Equ Appl Math 4 :100174, 2021). As a result of the refined decay estimate, we also improve a lower bound estimate of the radius of convergence of the Taylor expansion of $$T(cdot )f$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>(</mml:mo> <mml:mo>·</mml:mo> <mml:mo>)</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> in space and time. To refine the previous results, we show explicit pointwise estimates of higher order derivatives of the power function $$|xi |^{sig","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136015751","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 : 2023-09-19DOI: 10.1007/s00041-023-10039-x
Kristina Oganesyan
Abstract We prove the Hardy–Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample, which shows that if one slightly extends the considered class of coefficients, the Hardy–Littlewood relation fails.
{"title":"Two-Dimensional Hardy–Littlewood Theorem for Functions with General Monotone Fourier Coefficients","authors":"Kristina Oganesyan","doi":"10.1007/s00041-023-10039-x","DOIUrl":"https://doi.org/10.1007/s00041-023-10039-x","url":null,"abstract":"Abstract We prove the Hardy–Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample, which shows that if one slightly extends the considered class of coefficients, the Hardy–Littlewood relation fails.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135059297","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：