On the Rademacher maximal function

Mikko Kemppainen. "On the Rademacher maximal function." Studia Mathematica 203.1 (2011): 1-31. <http://eudml.org/doc/285508>.

@article{MikkoKemppainen2011,
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 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.},
author = {Mikko Kemppainen},
journal = {Studia Mathematica},
keywords = {R-boundedness; martingale; type; cotype; Rademacher maximal operator},
language = {eng},
number = {1},
pages = {1-31},
title = {On the Rademacher maximal function},
url = {http://eudml.org/doc/285508},
volume = {203},
year = {2011},
}

TY - JOUR
AU - Mikko Kemppainen
TI - On the Rademacher maximal function
JO - Studia Mathematica
PY - 2011
VL - 203
IS - 1
SP - 1
EP - 31
AB - 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.
LA - eng
KW - R-boundedness; martingale; type; cotype; Rademacher maximal operator
UR - http://eudml.org/doc/285508
ER -