Bases of wavelets and linear operators in anisotropic Lizorkin-Triebel spaces
type: Item
instance of: scholarly article
title: Bases of wavelets and linear operators in anisotropic Lizorkin-Triebel spaces
zbMATH Open document ID: 0885.42021
published in: Doklady Mathematics
publication date: 1998-04-20T00:00:00Z
review text: The authors construct unconditional wavelet bases in the anisotropic Lizorkin-Triebel spaces \(F^{(s)}_{pq}\) on \(\mathbb{R}^n\). With the aid of these bases they establish continuity of the anisotropic Calderón-Zygmund operators and anisotropic pseudo-differential operators, acting in \(F^{(s)}_{pq}\). As a consequence, certain refinements are obtained for the relevant results in the isotropic case, and applications to some classical operators (heat operator, the Hilbert transform) are given.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 1050688
zbMATH Keywords: wavelet bases
zbMATH Keywords: anisotropic Lizorkin-Triebel spaces
zbMATH Keywords: anisotropic Calderón-Zygmund operators
author: M. Z. Berkolajko
author: I. Ya. Novikov
reviewed by: Boris Rubin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1050688