Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings

Abstract

In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces ${\dot{B}}_{p,q}^s$ and Triebel-Lizorkin spaces ${\dot{F}}_{p,q}^s$ for all $s\in (0,1)$ and $p,q\in (n/(n+s),\infty ],$ both in ${\mathbb{R}}^n$ and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve ${\dot{F}}_{n/s,q}^s$ on $\rn$ for all $s\in (0,1)$ and $q\in (n/(n+s),\infty ]$. A metric measure space version of the above morphism property is also established.

Cited by in corpus (2)

• Classic and exotic Besov spaces induced by good grids
• The Besov Capacity In Metric Spaces