Homogeneous even kernels on surfaces
type: Item
instance of: scholarly article
title: Homogeneous even kernels on surfaces
zbMATH Open document ID: 0807.42014
DOI: 10.1007/BF02572315
published in: Mathematische Zeitschrift
publication date: 1994-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174644
review text: Let \(K(x)= {P_ k(x)\over | x|^{k+n}}\), where \(k\) is a positive integer, \(P_ k\) is a homogeneous polynomial of degree \(k\) defined on \(\mathbb{R}^{n+1}\). It was known previously that if \(P_ k\) is odd, then for a wide class of \(n\)-dimensional surfaces the principal value singular integral introduced by the kernel \(K\) defined on some nice classes of functions on these surfaces can be extended to \(L^ 2\)- bounded operators. In this paper we proved that for an even kernel of the given type, if the associated maximal integrals of the indicator functions on a set of \(n\)-dimensional surfaces are a.e. finite, and, if the set of surfaces has a set of tangent hyperplanes of a certain variety of directions, then the kernel must be identically zero.
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 704911
zbMATH Keywords: homogeneous even kernels
zbMATH Keywords: principle value singular integral
zbMATH Keywords: \(L^ 2\)- bounded operators
zbMATH Keywords: maximal integrals
author: Garth I. Gaudry
author: Tao Qian
MaRDI profile type: Publication
cites work: La solution des conjectures de Calderon
cites work: L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
cites work: A Criterion for the Boundedness of Singular Integrals on Hypersurfaces
cites work: Q5607484
cites work: Q5640160
description: scientific article; zbMATH DE number 704911