In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-2-4,
author = {Richard Lechner and Markus Passenbrunner},
title = {Adaptive Deterministic Dyadic Grids on Spaces of Homogeneous Type},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {62},
year = {2014},
pages = {139-159},
zbl = {1319.46029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-2-4}
}
Richard Lechner; Markus Passenbrunner. Adaptive Deterministic Dyadic Grids on Spaces of Homogeneous Type. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) pp. 139-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-2-4/