Analysis Seminar:Local and global Sobolev regularity of quasiconformal maps

Abstract: One important inspiration for weighted Lebesgue space bounds of singular integral operators is their application to quasiconformal and quasiregular maps through the Beurling-Ahlfors transform. The original results along these lines in the 0th order case were due to Astala-Iwaniec-Saksman and Petermichl-Volberg at the turn of the millennium. We extend these results using our recently developed weighted Sobolev theory of singular integral operators and their compressions to domains.