A martingale study of the Beurling-Ahlfors transform in \(\mathbb{R}^ n\)

DOI10.1006/jfan.1996.3022zbMath0876.60026OpenAlexW2046405348MaRDI QIDQ1354625

Arthur II Lindeman, Rodrigo Bañuelos

Publication date: 2 June 1997

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1996.3022

zbMATH Keywords

martingale transformsBeurling-Ahlfors transform

Mathematics Subject Classification ID

Martingales and classical analysis (60G46)

Related Items (15)

The foundational inequalities of D. L. Burkholder and some of their ramifications ⋮ Orthogonality in complex martingale spaces and connections with the Beurling-Ahlfors transform ⋮ Morrey's conjecture for the planar volumetric-isochoric split: least rank-one convex energy functions ⋮ Riesz transforms on compact Lie groups, spheres and Gauss space ⋮ Second order elliptic equations and Hodge-Dirac operators ⋮ Martingale transforms and \(L^p\)-norm estimates of Riesz transforms on complete Riemannian manifolds ⋮ Nonlinear Cauchy-Riemann operators in ℝⁿ ⋮ Quasiharmonic fields. ⋮ Riesz transforms on forms and \(L^p\)-Hodge decomposition on complete Riemannian manifolds ⋮ On the weak \(L ^{p }\)-Hodge decomposition and Beurling--Ahlfors transforms on complete Riemannian manifolds ⋮ Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space ⋮ Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular ⋮ Operator-valued martingale transforms ⋮ A note on second order Riesz transforms in \(3\)-dimensional Lie groups ⋮ Burkholder integrals, Morrey’s problem and quasiconformal mappings

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