Capacities and embeddings of Besov spaces via general convolution kernels

Hu, Rui; Zhai, Zhichun; Li, Pentago

Capacities and embeddings of Besov spaces via general convolution kernels

Author

Hu, Rui

Zhai, Zhichun

Li, Pentago

Date

2024

Keywords

Carleson embeddings, fractional Besov spaces, Lorentz spaces, nonnegative Radon measure

Abstract (summary)

This note is denoted to establish equivalent characterizations of Carleson embeddings of fractional Besov spaces Λp,q β (Rn) into the Lorentz spaces Lq0,pμ (R1+n+) induced by general convolution kernels Φt(·). When (p, q) ∈ (1, n/β) x (1,∞), the embeddings will be characterized in terms of capacitary type inequalities for open subsets of Rn. When p = q ∈ (0, 1], the embeddings will be characterized in terms of fractional Besov capacities or the associated variational functional of a nonnegative Radon measure μ. Especially, when p = q = 1 and β ∈ (0, 1), the characterization can be also established in terms of fractional perimeters.

Publication Information

Li, P., Hu, R., & Zhai, Z. (2024). Capacities and embeddings of Besov spaces via general convolution kernels. La Matematica, 3(1), 417–434. https://doi.org/10.1007/s44007-024-00091-4