Mean convergence of Fourier-Dunkl series

被引：8

作者：

Ciaurri, Oscar ^{[3
,4
]}

Perez, Mario ^{[1
,2
]}

Manuel Reyes, Juan ^{[5
]}

Luis Varona, Juan ^{[3
,4
]}

机构：

[1] Univ Zaragoza, IUMA, E-50009 Zaragoza, Spain

[2] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

[3] Univ La Rioja, CIME, Logrono 26004, Spain

[4] Univ La Rioja, Dept Matemat & Computac, Logrono 26004, Spain

[5] Univ Pompeu Fabra, Dept Tecnol, Barcelona 08003, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 372卷 / 02期

关键词：

Dunkl transform; Fourier-Dunkl series; Orthogonal system; Mean convergence; WEIGHTED NORM INEQUALITIES; TRANSFORM; THEOREM;

D O I：

10.1016/j.jmaa.2010.07.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the context of the Dunkl transform a complete orthogonal system arises in a very natural way. This paper studies the weighted norm convergence of the Fourier series expansion associated to this system. We establish conditions on the weights, in terms of the A(p) classes of Muckenhoupt, which ensure the convergence. Necessary conditions are also proved, which for a wide class of weights coincide with the sufficient conditions. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：470 / 485

页数：16

共 19 条

[1]

Andersen NB, 2005, INT MATH RES NOTICES, V2005, P1817

[2]

BENEDEK A, 1971, STUD APPL MATH, V50, P281

[3]

Benedek A., 1972, Rev. Union Mat. Argent., V26, P42

[4] The multiplier of the interval [-1,1] for the Dunkl transform on the real line [J].

Betancor, Jorge J. ;

Ciaurri, Oscar ;

Varona, Juan L. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 242 (01) :327-336

[5] A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform [J].

Ciaurri, Oscar ;

Varona, Juan L. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (09) :2939-2947

[6] THE DUNKL TRANSFORM [J].

DEJEU, MFE .

INVENTIONES MATHEMATICAE, 1993, 113 (01) :147-162

[7] INTEGRAL-KERNELS WITH REFLECTION GROUP INVARIANCE [J].

DUNKL, CF .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1991, 43 (06) :1213-1227

[8] MEAN AND WEAK-CONVERGENCE OF FOURIER-BESSEL SERIES [J].

GUADALUPE, JJ ;

PEREZ, M ;

RUIZ, FJ ;

VARONA, JL .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 173 (02) :370-389

[9] 2 NOTES ON CONVERGENCE AND DIVERGENCE AE OF FOURIER-SERIES WITH RESPECT TO SOME ORTHOGONAL SYSTEMS [J].

GUADALUPE, JJ ;

PEREZ, M ;

RUIZ, FJ ;

VARONA, JL .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 116 (02) :457-464

[10] WEIGHTED NORM INEQUALITIES FOR CONJUGATE FUNCTION AND HILBERT TRANSFORM [J].

HUNT, R ;

MUCKENHOUPT, B ;

WHEEDEN, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 176 (449) :227-251

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