The maximal operator of Bochner-Riesz means for radial functions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0977.42006
author: Sunggeum Hong
publication date: 2002-01-08T00:00:00Z
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B15
zbMATH DE Number: 1594802
zbMATH Keywords: maximal operator
zbMATH Keywords: Bochner-Riesz means
zbMATH Keywords: radial function
zbMATH Keywords: Lebesgue space
MaRDI profile type: Publication
title: The maximal operator of Bochner-Riesz means for radial functions
published in: Bulletin of the Korean Mathematical Society
review text: Let NEWLINE\[NEWLINES^\delta_\ast f(x)=\sup_{\varepsilon>0}(2\pi)^{-n} \left|\int_{{\mathbb{R}}^n}(1-|\varepsilon\xi|^2)^\delta_+\hat f(\xi) e^{i\langle x,\xi\rangle} d\xi\right|.NEWLINE\]NEWLINE The author proves that for \(n\geq 2\), \(0<\delta\leq (n-2)/2\) and \(p=2n/(n+1+2\delta)\), then \(S^\delta_\ast\) is of weak type \((p,p)\) on radial functions in \(L^p({\mathbb{R}}^n)\).
reviewed by: Dachun Yang
description: scientific article