Some remarks on the \(L^p\) estimates for powers of the Ahlfors-Beurling operator

DOI10.1007/s00013-011-0246-1zbMath1222.42017OpenAlexW2091750233MaRDI QIDQ543297

Oliver Dragičević

Publication date: 17 June 2011

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-011-0246-1

zbMATH Keywords

hypergeometric functionsAhlfors-Beurling transform

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Spectrum, resolvent (47A10)

Related Items (5)

The foundational inequalities of D. L. Burkholder and some of their ramifications ⋮ Sharp \(L^p\) estimates of powers of the complex Riesz transform ⋮ Weighted estimates for powers of the Ahlfors-Beurling operator ⋮ Distributions of anisotropic order and applications to H-distributions ⋮ Non-stretch mappings for a sharp estimate of the Beurling-Ahlfors operator

Cites Work

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• A rotation method which gives linear \(L^{p}\) estimates for powers of the Ahlfors--Beurling operator
• A proof of the Bieberbach conjecture
• $L^p$--bounds for the Beurling--Ahlfors transform
• Heating of the Ahlfors–Beurling operator, and estimates of its norm
• On singular integral and martingale transforms
• Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in L^p(C)

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