4,749 research outputs found
Regularity of the Hardy-Littlewood maximal operator on block decreasing functions
We study the Hardy-Littlewood maximal operator defined via an unconditional
norm, acting on block decreasing functions. We show that the uncentered maximal
operator maps block decreasing functions of special bounded variation to
functions with integrable distributional derivatives, thus improving their
regularity. In the special case of the maximal operator defined by the
l_infty-norm, that is, by averaging over cubes, the result extends to block
decreasing functions of bounded variation, not necessarily special.Comment: 26 page
Boundedness and unboundedness results for some maximal operators on functions of bounded variation
We characterize the space of functions of bounded variation on an
arbitrary interval , in terms of a uniform boundedness
condition satisfied by the local uncentered maximal operator from
into the Sobolev space .
By restriction, the corresponding characterization holds for . We
also show that if is open in , then boundedness from
into fails for the local directional maximal operator
, the local strong maximal operator , and the iterated local
directional maximal operator . Nevertheless, if
satisfies a cone condition, then boundedly, and the
same happens with , , and .Comment: 15 page
On maximal and potential operators with rough kernels in variable exponent spaces
In the framework of variable exponent Lebesgue and Morrey spaces we prove some boundedness results for operators with rough kernels, such as the maximal operator, fractional maximal operator, sharp maximal operators and fractional operators. The approach is based on some pointwise estimates
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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