Sobolev regularity of the Beurling transform on planar domains

DOI10.5565/PUBLMAT6121701zbMath1375.30026arXiv1507.04334OpenAlexW2214745984MaRDI QIDQ2405866

Martí Prats

Publication date: 28 September 2017

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.04334

zbMATH Keywords

Sobolev spacesquasiconformal mappingsLipschitz domainsBeurling transformDavid-Semmes betasPeter Jones' betas

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Quasiconformal mappings in the complex plane (30C62) Harmonic analysis and PDEs (42B37)

Related Items

Singular integral operators in Zygmund spaces on domains ⋮ Wavelet representation of singular integral operators ⋮ Weighted Sobolev estimates of the truncated Beurling operator ⋮ Sobolev regularity of the canonical solutions to \(\bar{\partial}\) on product domains ⋮ Sufficient conditions for C^1,α parametrization and rectifiability ⋮ Harmonic and Trace Inequalities in Lipschitz Domains ⋮ TheA-integral and restricted Ahlfors–Beurling transform ⋮ Dorronsoro's theorem in Heisenberg groups ⋮ DISCRETE AHLFORS-BEURLING TRANSFORM AND ITS PROPERTIES ⋮ Unnamed Item ⋮ Sobolev regularity of quasiconformal mappings on domains