Abstract
For each 1 ⩽ q < p we precisely evaluate the main Bellman functions associated with the local L p → L q estimates of the dyadic maximal operator on R n . Actually we do that in the more general setting of tree-like maximal operators and with respect to general convex and increasing growth functions. We prove that these Bellman functions equal to analogous extremal problems for the Hardy operator which can be viewed as a symmetrization principle for such operators. Under certain mild conditions on the growth functions we show that for the latter extremals exist (although for the original Bellman functions do not) and analyzing them we give a determination of the corresponding Bellman function.
Published Version
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