On the Rademacher maximal function

• Autorzy: Mikko Kemppainen
• Języki publikacji: EN

Abstrakty

EN

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 σ-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.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 42B25: Maximal functions, Littlewood-Paley theory
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 203
• Numer: 1
• Strony: 1-31

Daty

wydano

2011

Twórcy

autor

Mikko Kemppainen

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

Identyfikatory

DOI

10.4064/sm203-1-1