On weighted Lizorkin-Triebel spaces. Singular integrals, multipliers, imbedding theorems
type: Item
instance of: scholarly article
title: On weighted Lizorkin-Triebel spaces. Singular integrals, multipliers, imbedding theorems
zbMATH Open document ID: 0576.46023
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: The author considers the Lizorkin-Triebel type spaces \(L^{p,\theta}_{\omega,m}\) with a Muckenhoupt type weight function \(\omega\). He gives the theorems on Fourier multipliers for \(L^{p,\theta}_{\omega,m}\)-spaces. By means of the method of multipliers he develops the complete imbedding theory for \(L^{p,\theta}_{\omega,m}\)-spaces in the case of different metrics and of different dimensions. The author gives also the theorem on the boundedness of the maximal singular operator generated by an n-tuple singular operator in the space \(L^ p_{\omega}\). The exact characterization of weight functions \(\omega\) is given for an n-tuple singular integral operator to be bounded in the space \(L^ p_{\omega}\).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 3921263
zbMATH Keywords: Lizorkin-Triebel type spaces
zbMATH Keywords: Muckenhoupt type weight
zbMATH Keywords: Fourier multipliers
zbMATH Keywords: complete imbedding
zbMATH Keywords: maximal singular operator
author: Vakhtang Kokilashvili
reviewed by: S. G. Samko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3921263