A geometric approach to the Calderón-Zygmund estimates
type: Item
instance of: scholarly article
title: A geometric approach to the Calderón-Zygmund estimates
zbMATH Open document ID: 1026.31003
author: Lihe Wang
publication date: 2003-12-15T00:00:00Z
review text: This paper deals with a new proof of the classical Calderón-Zygmund estimates. Let \(B_r=\) \(\{x\in\mathbb{R}^n\mid|x|< r\}\) and \(u\) is a solution of \(\Delta u= f\) in \(B_2\). Then \[ \int_{B_1}|D^2 u|^2 dx\leq C\Biggl(\int_{B_2}|f|^p dx+ \int_{B_2}|u|^p dx\Biggr) \] for any \(1< p<+\infty\). In the proof the author uses among standard arguments the Vitali covering lemma and Hardy-Littlewood maximal function.
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1941610
zbMATH Keywords: Calderón-Zygmund estimates
zbMATH Keywords: Vitali covering lemma
zbMATH Keywords: Hardy-Littlewood maximal function
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s10114-003-0264-4
OpenAlex ID: W2318509154
cites work: Q5607484
cites work: Q4389910
cites work: Interior a priori estimates for solutions of fully nonlinear equations
cites work: On the regularity theory of fully nonlinear parabolic equations: II
cites work: Q4399897
cites work: On the existence of certain singular integrals
DOI: 10.1007/S10114-003-0264-4
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1941610