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/