Cauchy singular integral operator with parameters in Log-H\"older spaces
Complex Variables
2020-01-14 v1
Abstract
This paper is motivated by a claim in the classical textbook of Muskhelishvili concerning the Cauchy singular integral operator on H\"older functions with parameters. To the contrary of the claim, a counter example was constructed by Tumanov which shows that with parameters fails to maintain the same H\"older regularity with respect to the parameters. In view of the example, the behavior of the Cauchy singular integral operator with parameters between a type of Log-H\"older spaces is investigated to obtain the sharp norm estimates. At the end of the paper, we discuss its application to the problem on product domains.
Cite
@article{arxiv.2001.03778,
title = {Cauchy singular integral operator with parameters in Log-H\"older spaces},
author = {Yifei Pan and Yuan Zhang},
journal= {arXiv preprint arXiv:2001.03778},
year = {2020}
}