Geodesic
Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces
Antonios D. Melas 1   ; Eleftherios N. Nikolidakis 1   ; Dimitrios Cheliotis 1
1 Department of Mathematics University of Athens Panepistimiopolis 15784, Athens, Greece
Studia Mathematica, Tome 239 (2017) no. 1, pp. 1-16 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm8524-3-2017
Keywords: provide estimates bellman type functions dyadic maximal operator mathbb maximal operators martingales related weighted spaces using type symmetrization principle introduced dyadic maximal operator earlier works authors introduce certain conditions weight imply estimate maximal operator corresponding weighted space using known estimate maximal operator double maximal operator different measures related weight estimates above bellman type functions

Antonios D. Melas  1   ; Eleftherios N. Nikolidakis  1   ; Dimitrios Cheliotis  1

1 Department of Mathematics University of Athens Panepistimiopolis 15784, Athens, Greece 
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Antonios D. Melas; Eleftherios N. Nikolidakis; Dimitrios Cheliotis. Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces. Studia Mathematica, Tome 239 (2017) no. 1, pp. 1-16. doi: 10.4064/sm8524-3-2017

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