Imbedding and multiplier theorems for discrete Littlewood-Paley spaces
type: Item
instance of: scholarly article
title: Imbedding and multiplier theorems for discrete Littlewood-Paley spaces
zbMATH Open document ID: 0865.42009
author: Igor E. Verbitsky
published in: Pacific Journal of Mathematics
publication date: 1996-12-15T00:00:00Z
review text: Imbedding and multiplier theorems are proved for discrete Littlewood-Paley spaces introduced by M. Frazier and B. Jawerth in their theory of wavelet-type decompositions of Triebel-Lizorkin spaces. The corresponding inequalities for discrete spaces (defined in terms of characteristic functions of dyadic cubes, with respect to an arbitrary locally finite measure on the Euclidean space), are useful in the theory of tent spaces, weighted inequalities, duality theorems, interpolation by analytic and harmonic functions, etc. The proofs make use of vector-valued maximal inequalities, dyadic versions of the Carleson measure theorem, and Pisier's factorization lemma. Some more general inequalities are considered with an arbitrary family of measurable functions in place of characteristic functions of dyadic cubes, which occur in the factorization theory of operators.
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 950232
zbMATH Keywords: imbedding theorems
zbMATH Keywords: vector-valued maximal inequalities
zbMATH Keywords: factorization of operators
zbMATH Keywords: weighted inequalities
zbMATH Keywords: duality
zbMATH Keywords: multiplier theorems
zbMATH Keywords: discrete Littlewood-Paley spaces
zbMATH Keywords: Triebel-Lizorkin spaces
zbMATH Keywords: dyadic cubes
zbMATH Keywords: tent spaces
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.529
OpenAlex ID: W1532799889
DOI: 10.2140/PJM.1996.176.529
description: scientific article; zbMATH DE number 950232