On the symbol of the integral operator of the \(B\)-potential type with a single characteristic
type: Item
instance of: scholarly article
title: On the symbol of the integral operator of the \(B\)-potential type with a single characteristic
zbMATH Open document ID: 0907.47047
published in: Doklady Mathematics
publication date: 1999-02-15T00:00:00Z
review text: The author continues his studies of the Riesz \(B\)-potentials, connected with the Fourier-Bessel transforms (FBT) [see for example his paper in Dokl. Akad. Nauk SSSR 315, No. 2, 291-296 (1990; Zbl 0749.42008); 341, No. 2, 161-165 (1995; Zbl 0889.46033) and others]. He studies the convolution operators (with respect to the FBT) which are operators of \(B\)-potential type with some homogeneous characteristic. Basing on the reviewer's approach [Tr. Mat. Inst. Steklova 156, 157-222 (1980; Zbl 0448.42012); Transl. in Proc. Steklov Inst. Mat. 156, 173-243 (1983)] to invert potential-type operators, the author develops some counterpart of this approach in the situation of FBT-convolutions. He studies the corresponding symbol-function and in the elliptic case arrives at hypersingular integral operator with a homogeneous characteristic as an inverse operator.
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 1155289
zbMATH Keywords: function spaces
zbMATH Keywords: fractional smoothness
zbMATH Keywords: Riesz and Bessel type potentials
zbMATH Keywords: hypersingular integrals
zbMATH Keywords: generalized translation
zbMATH Keywords: Bessel differential operator
zbMATH Keywords: Fourier-Bessel transforms
zbMATH Keywords: convolution operators
zbMATH Keywords: invert potential-type operators
author: L. N. Lyakhov
reviewed by: S. G. Samko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1155289