Littlewood-Paley theorem for arbitrary intervals: weighted estimates
type: Item
instance of: scholarly article
title: Littlewood-Paley theorem for arbitrary intervals: weighted estimates
zbMATH Open document ID: 1178.42004
published in: Journal of Mathematical Sciences (New York)
publication date: 2009-11-13T00:00:00Z
review text: As stated by the author, the main result is as follows: ``Let \(1<r<2\) and let \(b\) be a weight on \({\mathbb R}\) such that \(b^{-1/(r-1)}\) satisfies the Muckenhoupt condition \(A_{r'/2}\) (\(r'\) is the exponent conjugate to \(r\)). If \(f_j\) are functions whose Fourier transforms are supported on mutually disjoint intervals, then \[ \Big\| \sum_j f_j\Big\|_{L^p({\mathbb R},b)}\leq C \Big\| \Big(\sum_j |f_j|^2\Big)^{1/2}\Big\|_{L^p({\mathbb R},b)} \] for \(0<p\leq r\).''
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 30H10
zbMATH DE Number: 5632941
zbMATH Keywords: Littlewood-Paley
zbMATH Keywords: weighted estimates
zbMATH Keywords: Muckenhoupt condition
author: S. V. Kislyakov
reviewed by: Joan Cerdà
MaRDI profile type: Publication
full work available at URL: s10958-009-9293-6
OpenAlex ID: W1999255594
cites work: A Littlewood-Paley inequality for arbitrary intervals
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cites work: Weights, sharp maximal functions and hardy spaces
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DOI: 10.1007/S10958-009-9293-6
description: scientific article; zbMATH DE number 5632941