Extremal sequences for the Bellman function of the dyadic maximal operator and applications to the Hardy operator

Abstract

We prove that the extremal sequences for the Bellman function of the dyadic maximal operator behave approximately as eigenfunctions of this operator for a specific eigenvalue. We use this result to prove the analogous one with respect to the Hardy operator.

arXiv commentPublished in the Canadian J. Math. An argument has been corrected in the end of the proof of Theorem 3. The results remain unchanged