On regularity and irregularity of certain holomorphic singular integral operators

10 Jan 2019 · Lanzani Loredana, Stein Elias M. ·

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 $n\geq 2$.