On the Rademacher maximal function

Volume 203 / 2011

Mikko Kemppainen Studia Mathematica 203 (2011), 1-31 MSC: Primary 46E40; Secondary 42B25, 46B09. DOI: 10.4064/sm203-1-1


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.


  • Mikko KemppainenDepartment of Mathematics and Statistics
    University of Helsinki
    Gustaf Hällströmin katu 2b
    FI-00014 Helsinki, Finland

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