Weighted norm inequalities for fractional maximal operators--a Bellman function approach

2013/11/23 by Banuelos, Rodrigo, Osekowski, Adam
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1311.6025

Abstract

We study classical weighted L^p→ 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-ε theorem," derived also with Bellman functions, we obtain the sharp inequality of Lacey, Moen, Pérez and Torres.

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