On the Rademacher maximal function
Functional Analysis
2011-06-09 v3
Abstract
This paper studies a new maximal operator introduced by Hyt\"onen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The L^p-boundedness of this operator depends on the range space; certain requirements on type and cotype are present for instance. The original Euclidean definition of the maximal function is generalized to sigma-finite measure spaces with filtrations and the L^p-boundedness is shown not to depend on the underlying measure space or the filtration. Martingale techniques are applied to prove that a weak type inequality is sufficient for L^p-boundedness and also to provide a characterization by concave functions.
Cite
@article{arxiv.0912.3358,
title = {On the Rademacher maximal function},
author = {Mikko Kemppainen},
journal= {arXiv preprint arXiv:0912.3358},
year = {2011}
}
Comments
23 pages, 4 figures, typos corrected, proofs of Lemma 5.3 and Theorem 7.3 revised