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Complex Analysis and Geometry Seminar

Singular integral operators with holomorphic kernels: counterexamples to the \(L^p\)-theory

Loredana Lanzani  (Syracuse University)

Location:  Hill 005
Date & time: Friday, 04 May 2018 at 10:30AM - 11:30AM

Abstract: In this talk I will discuss joint work with E. M. Stein (Princeton U.) concerning the Lebesgue space theory for a family of singular integral operators in complex Euclidean space whose integration kernels are holomorphic functions of the output variable. 

The main focus will be on counter-examples that show the optimality of the assumptions we make on the ambient domain (various kinds of convexity; boundary regularity). Specifically, I will first recall recently obtained counter-examples for the Cauchy-Leray integral for a family of pseudo-balls. I will then summarize work in progress that concerns the analysis of \(L^p\)-regularity for the Szego projection for the Diederich-Fornaess worm domain. 

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