Compact embeddings for fractional Sobolev spaces HWs,p in the Heisenberg group as sp < Q

Chunhong Liu; Xiaoxue Ji

doi:10.1117/12.3025783

8 April 2024 Compact embeddings for fractional Sobolev spaces HW^s,p in the Heisenberg group as sp < Q

Chunhong Liu, Xiaoxue Ji

Proceedings Volume 13090, International Conference on Computer Application and Information Security (ICCAIS 2023); 130900Q (2024) https://doi.org/10.1117/12.3025783
Event: International Conference on Computer Application and Information Security (ICCAIS 2023), 2023, Wuhan, China

Abstract

Liu [1] has already been proven a compact embedding from fractional Sobolev spaces HW^s,p (Ω) to L^q (Ω) , where Ω⊂Hⁿ is a bounded extension domain and q∈[1, p] . In this paper, we prove a compact embedding from fractional spaces HW^s,p(Ω) to L^q(Ω) under sp < Q , where Ω⊂Hⁿ is a bounded extension domain and q ∈ [1, p*). Moreover, we give a Sobolev embedding for fractional spaces in the Heisenberg group.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Chunhong Liu and Xiaoxue Ji "Compact embeddings for fractional Sobolev spaces HW^s,p in the Heisenberg group as sp < Q", Proc. SPIE 13090, International Conference on Computer Application and Information Security (ICCAIS 2023), 130900Q (8 April 2024); https://doi.org/10.1117/12.3025783

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