English

Non-collapsing condition and Sobolev embeddings for Haj{\l}asz-Besov spaces

Functional Analysis 2022-04-22 v1

Abstract

In this paper we will focus on understanding the relation between Sobolev embedding theorems for Haj{\l}asz-Besov spaces defined on a doubling metric measure space (Ω,d,μ)(\Omega,d,\mu) and the non-collapsing condition of the measure, i.e. infxΩμ(B(x,1))>0. \inf_{x\in\Omega}\mu(B(x,1))>0. We will also obtain embedding results for Haj{\l}asz-Besov spaces whose modulus of smoothness is generated by a rearrangement invariant quasi-norm.

Keywords

Cite

@article{arxiv.2204.09990,
  title  = {Non-collapsing condition and Sobolev embeddings for Haj{\l}asz-Besov spaces},
  author = {Joaquim Martin and Walter A. Ortiz},
  journal= {arXiv preprint arXiv:2204.09990},
  year   = {2022}
}