Non-collapsing condition and Sobolev embeddings for Hajłasz–Besov spaces

Abstract

In this paper we will focus on understanding the relationship between Sobolev embedding theorems for Hajłasz–Besov spaces defined on a doubling metric measure space (Ω,d,μ) and the non-collapsing condition of the measure, i.e. (Formula presented.) We will also obtain embedding results for Hajłasz–Besov spaces whose modulus of smoothness is generated by a rearrangement invariant quasi-norm.