Some remarks on the dyadic Rademacher maximal function
Functional Analysis
2014-06-06 v3
Abstract
Properties of a maximal function for vector-valued martingales were studied by the author in an earlier paper. Restricting here to the dyadic setting, we prove the equivalence between (weighted) L^p inequalities and weak type estimates, and discuss an extension to the case of locally finite Borel measures on R^n. In addition, to compensate for the lack of an L^\infty inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.
Cite
@article{arxiv.1208.1629,
title = {Some remarks on the dyadic Rademacher maximal function},
author = {Mikko Kemppainen},
journal= {arXiv preprint arXiv:1208.1629},
year = {2014}
}
Comments
11 pages, revised version, appeared in Colloquium Mathematicum