Search results for "Calderón reproducing formula"

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

2010

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.

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 spaceAnalysisMathematicsJournal of Functional Analysis
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