Abstract
Abstract We provide an alternative proof and expression of the Bellman function of the dyadic maximal operator in connection with the dyadic Carleson imbedding theorem, which appears in [A. D. Melas, The Bellman functions of dyadic-like maximal operators and related inequalities, Adv. Math. 192 2005, 2, 310–340]. We also evaluate the Bellman function of four variables of the dyadic maximal operator.
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