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arXiv · 0909.2072

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

Pekka Koskela·Dachun Yang·Yuan Zhou
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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 $p\in(n/(n+1),\infty)$, we give a new characterization of the Hajłasz-Sobolev spaces $\dot M^{1, p}({\mathbb R}^n)$ via a grand Littlewood-Paley function.

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BibTeXRIS

Pekka Koskela, Dachun Yang, Yuan Zhou. 2009-11-02. A Characterization of Hajłasz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions. https://arxiv.org/abs/0909.2072

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