Capacity in Besov and Triebel–Lizorkin spaces with generalized smoothness

Abstract

We prove a lower bound estimate for capacities in Hajłasz–Besov, Hajłasz–Triebel–Lizorkin and Hajłasz–Sobolev spaces with generalized smoothness defined on metric spaces in terms of Netrusov–Hausdorff content or Hausdorff content. These results are improvements of the results obtained in [Z. Li, D. Yang and W. Yuan, Lebesgue points of Besov and Triebel–Lizorkin spaces with generalized smoothness, Mathematics 9 2021, 10.3390/math9212724].