Astala's conjecture from the point of view of singular integrals on metric spaces

zbMATH Open1345.42021arXiv1112.6148MaRDI QIDQ2990295

Alexander Volberg

Publication date: 29 July 2016

Abstract: In the proof of Astala's conjecture on quasiconformal distortion obtained by Lacey--Sawyer--Uriarte-Tuero one of the key point is an estimate of the Ahlfors--Beurling operator in a certain weighted space. We show that the point of view of non-homogeneous Harmonic Analysis simplifies considerably this key point.

Full work available at URL: https://arxiv.org/abs/1112.6148

zbMATH Keywords

weightsmetric spacesCalderón-Zygmund operatorssingular integrals\(A_2\) conditionquasiconformal distortionnon-homogeneous harmonic analysis

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Quasiconformal mappings in the complex plane (30C62)

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