The Bellman function of the dyadic maximal operator in connection with the Dyadic Carleson Imbedding Theorem and related inequalities

Abstract

We provide an alternative proof of the expression of the Bellman function of the dyadic maximal operator in connection with the Dyadic Carleson Imbedding Theorem, which appears in [10]. We also state and prove a sharp integral inequality for this operator in connection with the above Bellman function, and give an application