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arXiv · 0912.3358

On the Rademacher maximal function

Mikko Kemppainen
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Abstract

This paper studies a new maximal operator introduced by Hytönen, 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.

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Mikko Kemppainen. 2011-01-22. On the Rademacher maximal function. https://arxiv.org/abs/0912.3358

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