On regularity and irregularity of certain holomorphic singular integral operators

Loredana Lanzani, Elias M. Stein

Abstract: We survey recent work and announce new results concerning two singular integral operators whose kernels are holomorphic functions of the output variable, specifically the Cauchy-Leray integral and the Cauchy-Szeg\H o projection associated to various classes of bounded domains in $\mathbb C^n$ with $n\geq 2$.

ArXiv: 1901.03402