Duke Mathematical Journal

Sharp inequalities for the Beurling–Ahlfors transform on radial functions

Rodrigo Bañuelos and Adam Osȩkowski

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Abstract

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

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

Dates
First available in Project Euclid: 24 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1359036938

Digital Object Identifier
doi:10.1215/00127094-1962649

Mathematical Reviews number (MathSciNet)
MR3018958

Zentralblatt MATH identifier
1277.60076

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

Citation

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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