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

Authors :: Strzelecki, Michał
Source :: Ann. Acad. Sci. Fenn. Math. 42 (2017), 73-93
Publication Year :: 2015
Abstract: We calculate the norms of the operators connected to the action of the Beurling-Ahlfors transform on radial function subspaces introduced by Ba\~nuelos 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 Ba\~nuelos and Janakiraman, Ba\~nuelos and Os\c{e}kowski, and Volberg for $1<p\leq 2$.<br />Comment: 19 pages