Weighted inequalities for the Bochner-Riesz means related to the Fourier-Bessel expansions

被引：2

作者：

Ciaurri, Oscar ^{[1
]}

Roncal, Luz ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 329卷 / 02期

关键词：

Fourier-Bessel series; Bochner-Riesz means; two-weight inequalities; weak type inequalities;

D O I：

10.1016/j.jmaa.2006.07.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove weighted inequalities for the Bochner-Riesz means for Fourier-Bessel series with more general weights w(x) than previously considered power weights. These estimates are given by using the local Ap theory and Hardy's inequalities with weights. Moreover, we also obtain weighted weak type (1, 1) inequalities. The case when w(x) = x(a) is sketched and follows as a corollary of the main result. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1170 / 1180

页数：11

共 9 条

[1] WEIGHTED WEAK TYPE HARDY INEQUALITIES WITH APPLICATIONS TO HILBERT-TRANSFORMS AND MAXIMAL FUNCTIONS [J].

ANDERSEN, KF ;

MUCKENHOUPT, B .

STUDIA MATHEMATICA, 1982, 72 (01) :9-26

[2]

[Anonymous], PREPRINT

[3] The Bochner-Riesz means for Fourier-Bessel expansions [J].

Ciaurri, O ;

Roncal, L .

JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 228 (01) :89-113

[4]

CIAURRI O, IN PRESS STUDIA MATH

[5] MEAN CONVERGENCE OF FOURIER-BESSEL SERIES [J].

HOCHSTADT, H .

SIAM REVIEW, 1967, 9 (02) :211-+

[6] HARDYS INEQUALITY WITH WEIGHTS [J].

MUCKENHOUPT, B .

STUDIA MATHEMATICA, 1972, 44 (01) :31-+

[7]

Muckenhoupt B., 1986, MEM AM MATH SOC, V356

[8]

Nowak A, 2006, TOHOKU MATH J, V58, P277

[9]

Watson G.N., 1966, TREATISE THEORY BESS

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