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

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

2009-09-11

arxiv.org/abs/0909.2072v2

Mathematics

Classical Analysis and ODEs

J. Funct. Anal. (to appear)

Scientific paper

In this paper, we establish the equivalence between the Haj{\l}asz-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 $p\in(n/(n+1),\infty)$, we give a new characterization of the Haj{\l}asz-Sobolev spaces $\dot M^{1, p}({\mathbb R}^n)$ via a grand Littlewood-Paley function.

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