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On regularity and irregularity of certain holomorphic singular integral operators. (English) Zbl 1482.32002

Ciatti, Paolo (ed.) et al., Geometric aspects of harmonic analysis. Proceedings of the INdAM meeting, Cortona, Italy, June 25–29, 2018. Cham: Springer. Springer INdAM Ser. 45, 467-479 (2021).
Summary: 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-Szegő projection associated to various classes of bounded domains in \(\mathbb{C}^n\) with \(n \geq 2\).
For the entire collection see [Zbl 1470.42001].

MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)
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