Titchmarsh theorems for Fourier transforms of Holder-Lipschitz functions on compact homogeneous manifolds

被引：31

作者：

Daher, Radouan ^{[1
]}

Delgado, Julio ^{[2
,3
]}

Ruzhansky, Michael ^{[2
,3
,4
]}

机构：

[1] Univ Hassan 2, Dept Math, BP 5366, Casablanca, Morocco

[2] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England

[3] Queen Mary Univ London, Sch Math Sci, Mile End Rd, London E1 4NS, England

[4] Univ Ghent, Dept Math Anal Log & Discrete Math, Krijgslaan 281 S8, B-9000 Ghent, Belgium

来源：

MONATSHEFTE FUR MATHEMATIK | 2019年 / 189卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Compact homogeneous manifolds; Compact Lie groups; Lipschitz functions;

D O I：

10.1007/s00605-018-1253-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we extend classical Titchmarsh theorems on the Fourier transform of Holder-Lipschitz functions to the setting of compact homogeneous manifolds. As an application, we derive a Fourier multiplier theorem for L2-Holder-Lipschitz spaces on compact Lie groups. We also derive conditions and a characterisation for Dini-Lipschitz classes on compact homogeneous manifolds in terms of the behaviour of their Fourier coefficients.

引用

页码：23 / 49

页数：27

共 45 条

[1]

Akylzhanov R, 2017, EURASIAN MATH J, V8, P10

[2] SMOOTHNESS AND ABSOLUTE CONVERGENCE OF FOURIER-SERIES IN COMPACT TOTALLY DISCONNECTED GROUPS [J].

BENKE, G .

JOURNAL OF FUNCTIONAL ANALYSIS, 1978, 29 (03) :319-327

[3]

BERNSTEIN S, 2009, CR HEBD ACAD SCI, V158, P1661

[4] MULTIPLIERS OF LIPSCHITZ-SPACES ON ZERO DIMENSIONAL GROUPS [J].

BLOOM, WR .

MATHEMATISCHE ZEITSCHRIFT, 1981, 176 (04) :485-488

[5] Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces [J].

Dasgupta, Aparajita ;

Ruzhansky, Michael .

BULLETIN DES SCIENCES MATHEMATIQUES, 2014, 138 (06) :756-782

[6] LP-BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS [J].

Delgado, Julio ;

Ruzhansky, Michael .

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2019, 18 (03) :531-559

[7] Schatten classes and traces on compact groups [J].

Delgado, Julio ;

Ruzhansky, Michael .

MATHEMATICAL RESEARCH LETTERS, 2017, 24 (04) :979-1003

[8] LP-nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups [J].

Delgado, Julio ;

Ruzhansky, Michael .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2014, 102 (01) :153-172

[9]

Duren P.L, 1970, THEORY H P SPACES

[10] Characterization of Dini-Lipschitz functions for the Helgason Fourier transform on rank one symmetric spaces [J].

El Ouadih, Salah ;

Daher, Radouan .

ADVANCES IN PURE AND APPLIED MATHEMATICS, 2016, 7 (04) :223-230

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