Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces
Volume 239 / 2017
Studia Mathematica 239 (2017), 1-16
MSC: Primary 42B25.
DOI: 10.4064/sm8524-3-2017
Published online: 7 July 2017
Abstract
We provide some new estimates for Bellman type functions for the dyadic maximal operator on $\mathbb {R}^{n}$ and for maximal operators on martingales related to weighted spaces. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors, we introduce certain conditions on the weight that imply an estimate for the maximal operator on the corresponding weighted space. Also using a well known estimate for the maximal operator by a double maximal operator with different measures related to the weight, we give new estimates for the above Bellman type functions.
