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

2022/04/21 by Joaquim Martı́n, Martin, Joaquim, Walter A. Ortiz +1
Mathematics · #Advanced Harmonic Analysis Research #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2204.09990

Abstract

In this paper we will focus on understanding the relation 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. inf_x∈Ωμ(B(x,1))gt;0. We will also obtain embedding results for Hajłasz-Besov spaces whose modulus of smoothness is generated by a rearrangement invariant quasi-norm.

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