Duke Mathematical Journal

Sharp inequalities for the Beurling–Ahlfors transform on radial functions

Rodrigo Bañuelos and Adam Osȩkowski

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For 1p2, we prove sharp weak-type (p,p)-estimates for the Beurling–Ahlfors operator acting on the radial function subspaces of Lp(C). A similar sharp Lp-result is proved for 1<p2. The results are derived from martingale inequalities which are of independent interest.

Article information

Duke Math. J., Volume 162, Number 2 (2013), 417-434.

First available in Project Euclid: 24 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G46: Martingales and classical analysis
Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)


Bañuelos, Rodrigo; Osȩkowski, Adam. Sharp inequalities for the Beurling–Ahlfors transform on radial functions. Duke Math. J. 162 (2013), no. 2, 417--434. doi:10.1215/00127094-1962649. https://projecteuclid.org/euclid.dmj/1359036938

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