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RESEARCH PRODUCT

A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions

Dachun YangPekka KoskelaYuan ZhouYuan Zhou

subject

Calderón reproducing formulaMathematics::Functional AnalysisPure mathematicsTopological tensor product010102 general mathematicsMathematical analysisMathematics::Classical Analysis and ODEsTriebel–Lizorkin spaceTriebel–Lizorkin space01 natural sciences010101 applied mathematicsUniform continuityFréchet spaceSobolev spacesInterpolation spaceBesov spaceBirnbaum–Orlicz space0101 mathematicsLp spaceAnalysisMathematics

description

Abstract In this paper, we establish the equivalence between the Hajlasz–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 Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.

yearjournalcountryeditionlanguage
2010-04-01Journal of Functional Analysis
https://doi.org/10.1016/j.jfa.2009.11.004