Lipschitz continuity in Muckenhoupt $\mathcal{A}_1$ weighted function spaces
Volume 92 / 2011
Banach Center Publications 92 (2011), 107-129
MSC: Primary 46E35; Secondary 42B35, 47B06.
DOI: 10.4064/bc92-0-8
Abstract
We study continuity envelopes of function spaces $\newcommand{\rn}{{\mathbb{R}^n}}\newcommand{\B}{{B^s_{p,q}}}\B(\rn,w)$ and $\newcommand{\rn}{{\mathbb{R}^n}}\newcommand{\F}{{F^s_{p,q}}}\F(\rn,w)$ where the weight belongs to the Muckenhoupt class $\mathcal{A}_1$. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.
