Some Entropy Bump Conditions for Fractional Maximal and Integral Operators

Abstract

We investigate weighted inequalities for fractional maximal operators and fractional integral operators. We work within the innovative framework of "entropy bounds" introduced by Treil--Volberg. Using techniques developed by Lacey and the second author, we are able to efficiently prove the weighted inequalities.

v2. Part of Theorem 1.1 from v1 was not true; we fixed the error. We thank Kabe Moen for pointing this out to us