%0 Journal Article
%T A Characterization of Haj£¿asz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions
%A Pekka Koskela
%A Dachun Yang
%A Yuan Zhou
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0909.2072v2