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Hankel Matrices Acting on the Dirichlet Space 作用于 Dirichlet 空间的汉克尔矩阵
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-09-12 DOI: 10.1007/s00041-024-10112-z
Guanlong Bao, Kunyu Guo, Fangmei Sun, Zipeng Wang
{"title":"Hankel Matrices Acting on the Dirichlet Space","authors":"Guanlong Bao, Kunyu Guo, Fangmei Sun, Zipeng Wang","doi":"10.1007/s00041-024-10112-z","DOIUrl":"https://doi.org/10.1007/s00041-024-10112-z","url":null,"abstract":"<p>The study of the infinite Hankel matrix acting on analytic function spaces dates back to the influential work of Nehari and Widom on the Hardy space <span>(H^2)</span>. Since then, it has been extensively generalized to other settings such as weighted Bergman spaces, Dirichlet type spaces, and Möbius invariant function spaces. Nevertheless, several fundamental operator-theoretic questions, including the boundedness and compactness, remain unresolved in the context of the Dirichlet space. Motivated by this, via Carleson measures, the Widom type condition, and the reproducing kernel thesis, we obtain: </p><ol>\u0000<li>\u0000<span>(i)</span>\u0000<p>necessary and sufficient conditions for bounded and compact operators induced by Hankel matrices on the Dirichlet space, thereby answering a folk question in this field (Galanopoulos et al. in Result Math 78(3) Paper No. 106, 2023);</p>\u0000</li>\u0000<li>\u0000<span>(ii)</span>\u0000<p>necessary and sufficient conditions for bounded and compact operators induced by Cesàro type matrices on the Dirichlet space.</p>\u0000</li>\u0000</ol><p> As a beneficial product, we find an intrinsic function-theoretic characterization of functions with positive decreasing Taylor coefficients in the function space <span>({mathcal {X}})</span> throughly studied by Arcozzi et al. (Lond Math Soc II Ser 83(1):1–18, 2011). In addition, we also show that a random Dirichlet function almost surely induces a compact Hankel type operator on the Dirichlet space.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187078","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
Maximal Integral Inequalities and Hausdorff–Young 最大积分不等式和豪斯多夫-杨
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-09-05 DOI: 10.1007/s00041-024-10111-0
Calixto P. Calderón, Alberto Torchinsky
{"title":"Maximal Integral Inequalities and Hausdorff–Young","authors":"Calixto P. Calderón, Alberto Torchinsky","doi":"10.1007/s00041-024-10111-0","DOIUrl":"https://doi.org/10.1007/s00041-024-10111-0","url":null,"abstract":"<p>We discuss the Hausdorff–Young inequality in the context of maximal integral estimates, including the case of Hermite and Laguerre expansions. We establish a maximal inequality for integral operators with bounded kernel on <span>({mathbb {R}})</span>, which in particular allows for the pointwise evaluation of these operators, including the Fourier transform, for functions in appropriate Lorentz and Orlicz spaces. In the case of the Hermite expansions we prove a refined Hausdorff–Young inequality, further sharpened by considering the maximal Hermite coefficients in place of the Hermite coefficients when estimating the appropriate Lorentz and Orlicz norms. We also consider the refined companion Hausdorff–Young inequality and Hardy–Littlewood type inequalities for the Hermite expansions. Similar results are proved for the Laguerre expansions.\u0000</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187083","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
$$L^p(mathbb {R}^d)$$ Boundedness for a Class of Nonstandard Singular Integral Operators 一类非标准奇异积分算子的 $$L^p(mathbb {R}^d)$$ 有界性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-09-05 DOI: 10.1007/s00041-024-10104-z
Jiecheng Chen, Guoen Hu, Xiangxing Tao
{"title":"$$L^p(mathbb {R}^d)$$ Boundedness for a Class of Nonstandard Singular Integral Operators","authors":"Jiecheng Chen, Guoen Hu, Xiangxing Tao","doi":"10.1007/s00041-024-10104-z","DOIUrl":"https://doi.org/10.1007/s00041-024-10104-z","url":null,"abstract":"<p>In this paper, let <span>(Omega )</span> be homogeneous of degree zero which has vanishing moment of order one, <i>A</i> be a function on <span>(mathbb {R}^d)</span> such that <span>(nabla Ain textrm{BMO}(mathbb {R}^d))</span>, we consider a class of nonstandard singular integral operators, <span>(T_{Omega ,,A})</span>, with rough kernel being of the form <span>( frac{Omega (x-y)}{vert x-yvert ^{d+1}}big (A(x)-A(y)-nabla A(y)(x-y)big ) )</span>. This operator is closely related to the Calderón commutator. We prove that, under the Grafakos-Stefanov minimum size condition <span>(GS_{beta }(S^{d-1}))</span> with <span>(2&lt;beta &lt;infty )</span> for <span>(Omega )</span>, <span>(T_{Omega ,,A})</span> is bounded on <span>(L^p(mathbb {R}^d))</span> for <i>p</i> with <span>(1+1/(beta -1)&lt; p &lt; beta )</span>.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187081","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
Remarks on Frames from Projective Representations of Locally Compact Groups 从局部紧凑群的投影表示谈框架
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-09-05 DOI: 10.1007/s00041-024-10108-9
Junyun Chen, Chuangxun Cheng
{"title":"Remarks on Frames from Projective Representations of Locally Compact Groups","authors":"Junyun Chen, Chuangxun Cheng","doi":"10.1007/s00041-024-10108-9","DOIUrl":"https://doi.org/10.1007/s00041-024-10108-9","url":null,"abstract":"<p>A projective representation of a locally compact group does phase retrieval if it admits a maximal spanning frame vector. In this paper, we provide a characterization of maximal spanning vectors for type I and square integrable irreducible projective representations of separable locally compact abelian groups. This generalizes the well-known criterion for the time–frequency case and unifies previous criteria for finite groups case and locally compact Gabor case. As an application, we show that irreducible projective representations of compact abelian groups do phase retrieval.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187080","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
Approximation by Subsequences of Matrix Transform Means of Some Two-Dimensional Rectangle Walsh–Fourier Series 某些二维矩形沃尔什-傅里叶级数的矩阵变换手段的后继逼近
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-09-05 DOI: 10.1007/s00041-024-10106-x
István Blahota, György Gát
{"title":"Approximation by Subsequences of Matrix Transform Means of Some Two-Dimensional Rectangle Walsh–Fourier Series","authors":"István Blahota, György Gát","doi":"10.1007/s00041-024-10106-x","DOIUrl":"https://doi.org/10.1007/s00041-024-10106-x","url":null,"abstract":"<p>In the present paper we discuss the rate of the approximation by the matrix transform of special partial sums of some two-dimensional rectangle (decreasing diagonal) Walsh-Fourier series in <span>(L^p(G^{2}))</span> space (<span>(1le p &lt;infty )</span>) and in <span>(C(G^{2}))</span>. It implies in some special case </p><p>norm convergence. We also show an application of our results for Lipschitz functions. At the end of the paper we show the most important result, the almost everywhere convergence theorem. We note that <i>T</i> summation is a common generalization of the following known summation methods Cesàro, Weierstrass, Riesz and Picar and Bessel methods.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187082","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
Matrix Spherical Functions on Finite Groups 有限群上的矩阵球面函数
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-09-05 DOI: 10.1007/s00041-024-10110-1
C. Blanco Villacorta, I. Pacharoni, J. A. Tirao
{"title":"Matrix Spherical Functions on Finite Groups","authors":"C. Blanco Villacorta, I. Pacharoni, J. A. Tirao","doi":"10.1007/s00041-024-10110-1","DOIUrl":"https://doi.org/10.1007/s00041-024-10110-1","url":null,"abstract":"<p>In this paper we focus our attention on matrix or operator-valued spherical functions associated to finite groups (<i>G</i>, <i>K</i>), where <i>K</i> is a subgroup of <i>G</i>. We introduce the notion of matrix-valued spherical functions on <i>G</i> associated to any <i>K</i>-type <span>(delta in hat{K})</span> by means of solutions of certain associated integral equations. The main properties of spherical functions are established from their characterization as eigenfunctions of right convolution multiplication by functions in <span>(A[G]^K)</span>, the algebra of <i>K</i>-central functions in the group algebra <i>A</i>[<i>G</i>]. The irreducible representations of <span>(A[G]^K)</span> are closely related to the irreducible spherical functions on <i>G</i>. This allows us to study and compute spherical functions via the representations of this algebra.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187079","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
The Density Theorem for Operator-Valued Frames via Square-Integrable Representations of Locally Compact Groups 通过局部紧凑群的平方不可穷举表示的算子值帧密度定理
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-08-28 DOI: 10.1007/s00041-024-10107-w
Jingsheng Wang, Pengtong Li, Deguang Han
{"title":"The Density Theorem for Operator-Valued Frames via Square-Integrable Representations of Locally Compact Groups","authors":"Jingsheng Wang, Pengtong Li, Deguang Han","doi":"10.1007/s00041-024-10107-w","DOIUrl":"https://doi.org/10.1007/s00041-024-10107-w","url":null,"abstract":"<p>In this paper, we first prove a density theorem for operator-valued frames via square-integrable representations restricted to closed subgroups of locally compact groups, which is a natural extension of the density theorem in classical Gabor analysis. More precisely, it is proved that for such an operator-valued frame, the index subgroup is co-compact if and only if the generator is a Hilbert–Schmidt operator. Then we present some applications of this density theorem, and in particular establish necessary and sufficient conditions for the existence of such operator-valued frames with Hilbert–Schmidt generators. We also introduce the concept of wavelet transform for Hilbert–Schmidt operators, and use it to prove that if the representation space is infinite-dimensional, then the system indexed by the entire group is Bessel system but not a frame for the space of all Hilbert–Schmidt operators on the representation space.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187084","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
Heat Properties for Groups 组的热性能
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-08-14 DOI: 10.1007/s00041-024-10103-0
Erik Bédos, Roberto Conti
{"title":"Heat Properties for Groups","authors":"Erik Bédos, Roberto Conti","doi":"10.1007/s00041-024-10103-0","DOIUrl":"https://doi.org/10.1007/s00041-024-10103-0","url":null,"abstract":"<p>We revisit Fourier’s approach to solve the heat equation on the circle in the context of (twisted) reduced group C*-algebras, convergence of Fourier series and semigroups associated to negative definite functions. We introduce some heat properties for countably infinite groups and investigate when they are satisfied. Kazhdan’s property (T) is an obstruction to the weakest property, and our findings leave open the possibility that this might be the only one. On the other hand, many groups with the Haagerup property satisfy the strongest version. We show that this heat property implies that the associated heat problem has a unique solution regardless of the choice of the initial datum.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187085","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 New Class of FBI Transforms and Applications 新型联邦调查局变换及其应用
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-08-08 DOI: 10.1007/s00041-024-10102-1
G. Hoepfner, R. Medrado
{"title":"A New Class of FBI Transforms and Applications","authors":"G. Hoepfner, R. Medrado","doi":"10.1007/s00041-024-10102-1","DOIUrl":"https://doi.org/10.1007/s00041-024-10102-1","url":null,"abstract":"<p>We introduce a class of FBI transforms using weight functions (which includes the subclass of Sjöstrand’s FBI transforms used by Christ in (Commun Partial Differ Equ 22(3–4):359–379, 1997)) that is well suited when dealing with ultradifferentiable functions (see Definition 2.3) and ultradistributions (see Definition 2.15) defined by weight functions in the sense of Braun, Meise and Taylor (BMT). We show how to characterize local regularity of BMT ultradistributions using this wider class of FBI transform and, as an application, we characterize the BMT vectors (see Definition 1.2) and prove a relation between BMT local regularity and BMT vectors.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935435","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
Existence of Extremals for a Fourier Restriction Inequality on the One-Sheeted Hyperboloid 单片超球面上傅里叶限制不等式的极值存在性
IF 1.2 3区 数学
Journal of Fourier Analysis and Applications Pub Date : 2024-07-31 DOI: 10.1007/s00041-024-10090-2
René Quilodrán
{"title":"Existence of Extremals for a Fourier Restriction Inequality on the One-Sheeted Hyperboloid","authors":"René Quilodrán","doi":"10.1007/s00041-024-10090-2","DOIUrl":"https://doi.org/10.1007/s00041-024-10090-2","url":null,"abstract":"<p>We prove the existence of functions that extremize the endpoint <span>(L^2)</span> to <span>(L^4)</span> adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space <span>(mathbb {R}^4)</span> and that, taking symmetries into consideration, any extremizing sequence has a subsequence that converges to an extremizer.\u0000</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867748","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
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