A Characterization of Hajłasz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions

2009/09/11 by Pekka Koskela, Dachun Yang, Koskela, Pekka +3
Mathematics · #42B25 #42B30 (Secondary) #42B35 (Primary) #46E35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:42B25 #msc:42B30 #msc:42B35 #msc:46E35

paper · pdf · doi:10.48550/arxiv.0909.2072

J. Funct. Anal. (to appear)

arxiv created 2009/11/02 · arxiv updated 2009/12/01

Abstract

In this paper, we establish the equivalence between the Hajłasz-Sobolev spaces or classical Triebel-Lizorkin spaces and a class of grand Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p∈(n/(n+1),∞), we give a new characterization of the Hajłasz-Sobolev spaces M^{1, p}(\mathbb Rⁿ) via a grand Littlewood-Paley function.

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