%0 Journal Article
%T Weighted norm inequalities for fractional maximal operators--a Bellman function approach
%A Rodrigo Banuelos
%A Adam Osekowski
%J Mathematics
%D 2013
%I arXiv
%X We study classical weighted $L^p\to L^q$ inequalities for the fractional maximal operators on $\R^d$, proved originally by Muckenhoupt and Wheeden in the 70's. We establish a slightly stronger version of this inequality with the use of a novel extension of Bellman function method. More precisely, the estimate is deduced from the existence of a certain special function which enjoys appropriate majorization and concavity. From this result and an explicit version of the ``$A_{p-\varepsilon}$ theorem," derived also with Bellman functions, we obtain the sharp inequality of Lacey, Moen, P\'erez and Torres.
%U http://arxiv.org/abs/1311.6025v1