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Mathematics > Functional Analysis

arXiv:0912.3358 (math)
[Submitted on 17 Dec 2009 (v1), last revised 22 Jan 2011 (this version, v3)]

Title:On the Rademacher maximal function

Authors: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.
Comments: 23 pages, 4 figures, typos corrected, proofs of Lemma 5.3 and Theorem 7.3 revised
Subjects: Functional Analysis (math.FA)
MSC classes: 46E40 (Primary), 42B25 (Secondary)
Cite as: arXiv:0912.3358 [math.FA]
  (or arXiv:0912.3358v3 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.0912.3358
Journal reference: Studia Math., 203(1):1-31, 2011

Submission history

From: Mikko Kemppainen K [view email]
[v1] Thu, 17 Dec 2009 10:24:33 UTC (39 KB)
[v2] Mon, 15 Feb 2010 15:05:36 UTC (39 KB)
[v3] Sat, 22 Jan 2011 09:23:13 UTC (43 KB)
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