Analytic continuation and convolution of hypersingular higher Hilbert- Riesz kernels
type: Item
instance of: scholarly article
title: Analytic continuation and convolution of hypersingular higher Hilbert- Riesz kernels
zbMATH Open document ID: 0621.44007
DOI: 10.1016/0022-247X(87)90321-0
author: Peter Wagner
author: Juan Horváth
author: Norbert Ortner
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The usual higher Hilbert-Riesz transforms are principal value convolution transforms with kernels \(Y_ j(x)| x|^{-j-n}\), where \(Y_ j\) is a homogeneous harmonic polynomial of degree j. The authors consider more generally the kernel \(x^ j| x|^{-j+\lambda -n}\), where for Re \(\lambda\) \(<0\), the expression is defined as a distribution by analytic continuation, and obtain a condition under which two such kernels can be convolved and formulas for the convolution.
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 46F12
zbMATH DE Number: 4006946
zbMATH Keywords: Laplace operator
zbMATH Keywords: hypersingular Hilbert-Riesz transforms
zbMATH Keywords: higher Hilbert- Riesz transforms
zbMATH Keywords: convolution transforms
reviewed by: Y. Tanno
MaRDI profile type: Publication
cites work: Q3265951
cites work: Singular Integral Operators and Spherical Harmonics
cites work: Basic Sets of Polynomial Solutions for Partial Differential Equations
cites work: On Some Composition Formulas
cites work: Q5667105
cites work: Q4042146
cites work: Q4054243
cites work: Composition of hypersingular integral operators
cites work: Q3940314
cites work: Faltung hypersingulärer Integraloperatoren
cites work: Q3858794
cites work: Q3941867
cites work: Q5528072
cites work: Q5607484
cites work: Q5640160
full work available at URL: 0022-247x(87)90321-0
OpenAlex ID: W2067495225
description: scientific article; zbMATH DE number 4006946