English

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.

Keywords

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

R2 v1 2026-06-21T21:47:50.071Z