Regularity of \(\mathcal C^1\) and Lipschitz domains in terms of the Beurling transform

DOI10.1016/j.matpur.2012.10.014zbMath1284.44001arXiv1201.5403OpenAlexW2152244891MaRDI QIDQ388174

Xavier Tolsa

Publication date: 19 December 2013

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.5403

zbMATH Keywords

Sobolev spaceBesov spaceLipschitz domainBeurling transform

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (8)

Regularity of the Beurling transform in smooth domains ⋮ Weighted Sobolev estimates of the truncated Beurling operator ⋮ TheA-integral and restricted Ahlfors–Beurling transform ⋮ Restricted Beurling transforms on Campanato spaces ⋮ DISCRETE AHLFORS-BEURLING TRANSFORM AND ITS PROPERTIES ⋮ Unnamed Item ⋮ Sobolev regularity of quasiconformal mappings on domains ⋮ A T(P) theorem for Sobolev spaces on domains

Cites Work

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• Beltrami Equation with Coefficient in Sobolev and Besov Spaces
• Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs
• Mean Oscillation and Besov Spaces

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