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arXiv · 2608.23291

Essentially semi-commuting singular integral operators with Cauchy kernel on $L^{2}$

Chongchao Wang
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Abstract

In this paper, we completely characterize when the semi-commutator of two Cauchy singular integral operators on $L^2$ is compact. Our main idea is to study Cauchy singular integral operators via Hankel operators, Toeplitz operators and function algebras. Moreover, we obtain a necessary and sufficient condition for Cauchy singular integral operators to be essentially normal.

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Chongchao Wang. 2026-08-24. Essentially semi-commuting singular integral operators with Cauchy kernel on $L^{2}$. https://arxiv.org/abs/2608.23291

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