Geometric maximal operators and BMO on product bases
Functional Analysis
2020-07-29 v1
Abstract
We consider the problem of the boundedness of maximal operators on BMO on shapes in . We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, generalising a known result of Bennett for the basis of cubes. When the basis of shapes does not possess an engulfing property but exhibits a product structure with respect to lower-dimensional shapes coming from bases that do possess an engulfing property, we show that the corresponding maximal function is bounded from BMO to a space we define and call rectangular BLO.
Keywords
Cite
@article{arxiv.2007.13908,
title = {Geometric maximal operators and BMO on product bases},
author = {Galia Dafni and Ryan Gibara and Hong Yue},
journal= {arXiv preprint arXiv:2007.13908},
year = {2020}
}