Estimation of norms of singular integral operators in \(L^ p\) spaces with weights, satisfying Muckenhoupt's condition
type: Item
instance of: scholarly article
title: Estimation of norms of singular integral operators in \(L^ p\) spaces with weights, satisfying Muckenhoupt's condition
zbMATH Open document ID: 0624.47025
DOI: 10.1007/BF00970224
author: B. V. Pal'tsev
published in: Siberian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: There are considered spaces \(L^ p(R^ n;w)\), \(p>1\), with the norm \(\| f\|_{p,w}=(\int_{R^ n}| f(x)|^ pw(x)dx)^{1/p}\) in the case when the weights w satisfy the following condition, called the Muckenhoupt condition: \[ \int_{Q}w(x)dx(\int_{Q}w^{-(p-1)-1}(x)dx)^{p-1}\leq K_ p| Q|^ p \] for an arbitrary cube \(Q\subset R^ n\), with a constant \(K_ p\) which does not depend on Q. There are given some estimations of norms of Calderon-Zygmund operators in these spaces.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 45E99
Mathematics Subject Classification ID: 47Gxx
zbMATH DE Number: 4013355
zbMATH Keywords: weighted \(L^ p\)-space
zbMATH Keywords: weights
zbMATH Keywords: Muckenhoupt condition
zbMATH Keywords: Calderon-Zygmund operators
reviewed by: Danuta Przeworska-Rolewicz
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00970224
OpenAlex ID: W2312786666
description: scientific article; zbMATH DE number 4013355