## Duke Mathematical Journal

### Sharp inequalities for the Beurling–Ahlfors transform on radial functions

#### Abstract

For $1\leq p\leq2$, we prove sharp weak-type $(p,p)$-estimates for the Beurling–Ahlfors operator acting on the radial function subspaces of $L^{p}(\mathbb{C})$. A similar sharp $L^{p}$-result is proved for $1\lt p\leq2$. 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

#### 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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