This paper studies a new maximal operator introduced by Hytönen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The -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 σ-finite measure spaces with filtrations and the -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 -boundedness and also to provide a characterization by concave functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-1-1,
author = {Mikko Kemppainen},
title = {On the Rademacher maximal function},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {1-31},
zbl = {1228.46036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-1-1}
}
Mikko Kemppainen. On the Rademacher maximal function. Studia Mathematica, Tome 204 (2011) pp. 1-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-1-1/