arXiv Analytics

Sign in

arXiv:2411.19153 [math.FA]AbstractReferencesReviewsResources

Regularity of Characteristic Functions in Besov-Type and Triebel--Lizorkin-Type Spaces

Wen Yuan, Winfried Sickel, Dachun Yang

Published 2024-11-28Version 1

In this article, the authors determine the optimal regularity of characteristic functions in Besov-type and Triebel--Lizorkin-type spaces under restrictions on the measure of the $\delta$-neighborhoods of the boundary. In particular, the necessary and sufficient conditions for the membership in these spaces of characteristic functions of the snowflake domain and also some spiral type domains are obtained.

Comments: 59 pages, Submitted
Categories: math.FA, math.AP, math.CA
Subjects: 46E35, 42C15
Related articles: Most relevant | Search more
arXiv:2312.13549 [math.FA] (Published 2023-12-21)
Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces III: Characterizations of Molecules and Wavelets, Trace Theorems, and Boundedness of Pseudo-Differential Operators and Calderón--Zygmund Operators
arXiv:2304.00292 [math.FA] (Published 2023-04-01)
Matrix-Weighted Besov-Type and Triebel-Lizorkin-Type Spaces
arXiv:2001.02046 [math.FA] (Published 2020-01-07)
Compact embeddings in Besov-type and Triebel-Lizorkin-type Spaces on bounded domains

Links

Toolbox