The Bochner-Riesz means for Fourier-Bessel expansions: Norm inequalities for the maximal operator and almost everywhere convergence

JOURNAL OF APPROXIMATION THEORY

卷:167

Article

Ciaurri, Oscar¹  Roncal, Luz¹ 

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

关键词: Fourier-Bessel expansions;    Bochner-Riesz means;    Almost everywhere convergence;    Maximal operators;    Weighted inequalities;   

DOI  :  10.1016/j.jat.2012.11.012

来源: Elsevier

【 摘 要 】

In this paper, we develop a thorough analysis of the boundedness properties of the maximal operator for the Bochner-Riesz means related to the Fourier-Bessel expansions. For this operator, we study weighted and unweighted inequalities in the spaces L-P ((0, 1), x(2v+1) dx). Moreover, weak and restricted weak type inequalities are obtained for the critical values of p. As a consequence, we deduce the almost everywhere pointwise convergence of these means. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free