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• # Artykuł - szczegóły

## Studia Mathematica

2011 | 203 | 1 | 1-31

## On the Rademacher maximal function

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.

1-31

wydano
2011

### Twórcy

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