The L^p-norms of the Beurling-Ahlfors transform on radial functions

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 Osȩkowski, and Volberg for $1<p\le 2$.

19 pages

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