Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 73-93

THE L^p-NORMS OF THE BEURLING–AHLFORS TRANSFORM ON RADIAL FUNCTIONS

Michal Strzelecki

University of Warsaw, Institute of Mathematics
Banacha 2, 02–097 Warsaw, Poland; m.strzelecki 'at' mimuw.edu.pl

Abstract. We calculate the norms of the operators connected to the action of the Beurling–Ahlfors transform on radial function subspaces introduced by Bañuelos and Janakiraman. In particular, we find the norm of the Beurling–Ahlfors transform acting on radial functions for p > 2, extending the results obtained by Bañuelos and Janakiraman, Bañuelos and Osekowski, and Volberg for 1 < p ≤ 2.

2010 Mathematics Subject Classification: Primary 60G46; Secondary 42B20.

Key words: Beurling–Ahlfors transform, Hardy operator, L^p-norms, martingales, radial functions.

Reference to this article: M. Strzelecki: The L^p-norms of the Beurling–Ahlfors transform on radial functions. Ann. Acad. Sci. Fenn. Math. 42 (2017), 73-93.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4204

THE Lp-NORMS OF THE BEURLING–AHLFORS TRANSFORM ON RADIAL FUNCTIONS

Michal Strzelecki

THE L^p-NORMS OF THE BEURLING–AHLFORS TRANSFORM ON RADIAL FUNCTIONS