The Sobolev theorem for anisotropic Riesz-Bessel potentials in Morrey-Bessel spaces
type: Item
instance of: scholarly article
title: The Sobolev theorem for anisotropic Riesz-Bessel potentials in Morrey-Bessel spaces
zbMATH Open document ID: 0982.46023
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The Morrey-Bessel space \(L^\gamma_{p,\lambda}(\mathbb{R}^n_+)\) is defined as the space of measurable functions \(f\) on \(\mathbb{R}^n_+\) for which the norm \(\|f\|_{L^\gamma_{p,\lambda}}= \sup_{x,t} (t^{-\lambda} \int_{E_t}|T^y f(x)|^p dy)^{1/p}< \infty\), \(E_t\) being some distribution function and \(T^y f(x)\) -- a generalized shift operator. The main result is the inequality \(\|R^\alpha_B f\|_{L^\gamma_{p,\lambda}}\leq C_{p,\lambda}\|f\|_{L^\gamma_{p,\lambda}}\), where \(R_Bf(x)\) is the unisotropic Riesz-Bessel potential of \(f\). No proofs are given.
reviewed by: Julian Musielak
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 1557748
zbMATH Keywords: Sobolev theorem
zbMATH Keywords: Morrey-Bessel space
zbMATH Keywords: generalized shift operator
zbMATH Keywords: unisotropic Riesz-Bessel potential
author: Vagif S. Guliyev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1557748