59,876 research outputs found
Sharp Lorentz estimates for dyadic-like maximal operators and related Bellman functions
We precisely evaluate Bellman type functions for the dyadic maximal opeator
on and of maximal operators on martingales related to local Lorentz type
estimates. Using a type of symmetrization principle, introduced for the dyadic
maximal operator in earlier works of the authors we precisely evaluate the
supremum of the Lorentz quasinorm of the maximal operator on a function
when the integral of is fixed and also the same Lorentz quasinorm of
is fixed. Also we find the corresponding supremum when the integral of
is fixed and several weak type conditions are given.Comment: 11 page
Local lower norm estimates for dyadic maximal operators and related Bellman functions
We provide lower and weak -bounds for the localized dyadic maximal
operator on , when the local and the local norm of the
function are given. We actually do that in the more general context of homo-
geneous tree-like families in probability spaces.Comment: 9 page
Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces
We provide some new estimates for Bellman type functions for the dyadic
maximal opeator on and of 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 estimate for the maximal operator on the
corresponding weighted space. Also using a well known estimate for the maximal
operator by a double maximal operators on different m easures related to the
weight we give new estimates for the above Bellman type functions.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1511.0611
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