Two discrete fractional integral operators revisited
type: Item
instance of: scholarly article
title: Two discrete fractional integral operators revisited
zbMATH Open document ID: 1029.39016
DOI: 10.1007/BF02868485
author: Stephen Wainger
author: Elias M. Stein
published in: Journal d'Analyse Mathématique
publication date: 2003-09-11T00:00:00Z
review text: For the operator \(I_\lambda f(m)= \sum^\infty_{n=1} f(m- n^2)n^\lambda\) the norm estimate \(\|I_\lambda f\|_{\ell^p}\leq A\|f\|_{\ell^q}\) is proved for certain \(\lambda\), \(p\), \(q\), in particular, for \(\lambda= 1+ i\gamma\) and \(p= q\). Also a two-dimensional generalization is treated.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 1931239
zbMATH Keywords: discrete fractional integral operators
zbMATH Keywords: norm estimate
reviewed by: Lothar Berg
MaRDI profile type: Publication
cites work: Calderón-Zygmund operators on product spaces
cites work: Discrete analogues in harmonic analysis: spherical averages
cites work: Two discrete fractional integrals
cites work: A Littlewood-Paley inequality for arbitrary intervals
cites work: Discrete analogues of singular Radon transforms
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cites work: Q5827024
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description: scientific article; zbMATH DE number 1931239