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On the symmetrization of Cauchy-like kernels

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If you have a question about this talk, please contact Alessio Martini.

In this talk I will present new symmetrization identities for a family of Cauchy-like kernels in complex dimension one.

Symmetrization identities of this kind were first employed in geometric measure theory by P. Mattila, M. Melnikov, X. Tolsa, J. Verdera et al., to obtain a new proof of L2(μ) regularity of the Cauchy transform (with μ a positive Radon measure in C), which ultimately led to the partial resolution of a long-standing open problem known as the Vitushkin’s conjecture.

Here we extend this analysis to a class of kernels that are more closely related to the holomorphic reproducing kernels that arise in complex function theory.

This is joint work with Malabika Pramanik (U. British Columbia).

This talk is part of the Analysis seminar series.

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