Embeddings of doubling weighted Besov spaces
Volume 102 / 2014
Banach Center Publications 102 (2014), 105-119
MSC: Primary 46E35.
DOI: 10.4064/bc102-0-7
Abstract
We study continuous embeddings of Besov spaces of type $B_{p,q}^s(\mathbb{R}^n,w)$, where $s\in\mathbb{R}$, $0< p< \infty$, $0< q\leq\infty$, and the weight $w$ is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.
