On singular integrals of Calderón-type in \(\mathbb{R}^ n\), and BMO
type: Item
instance of: scholarly article
title: On singular integrals of Calderón-type in \(\mathbb{R}^ n\), and BMO
zbMATH Open document ID: 0874.42011
DOI: 10.4171/RMI/159
author: Steve Hofmann
published in: Revista Matemática Iberoamericana
publication date: 1995-04-11T00:00:00Z
full work available at URL: https://eudml.org/doc/39463
review text: Summary: 0e prove \(L^p\) (and weighted \(L^p\)) bounds for singular integrals of the form \[ \text{p.v. } \int_{\mathbb{R}^n} E\Biggl({A(x)- A(y)\over|x-y|}\Biggr) {\Omega(x- y)\over|x-y|^n} f(y)dy, \] where \(E(t)=\cos t\) if \(\Omega\) is odd, and \(E(t)=\sin t\) if \(\Omega\) is even, and where \(\nabla A\in\text{BMO}\). Even in the case that \(\Omega\) is smooth, the theory of singular integrals with ``rough'' kernels plays a key role in the proof. By standard techniques, the trigonometric function \(E\) can then be replaced by a large class of smooth functions \(F\). Some related operators are also considered. As a further application, we prove a compactness result for certain layer potentials.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 722305
zbMATH Keywords: singular integrals of Calderón-type
zbMATH Keywords: BMO
zbMATH Keywords: compactness
zbMATH Keywords: layer potentials
MaRDI profile type: Publication
OpenAlex ID: W159464633
description: scientific article; zbMATH DE number 722305