Problems on averages and lacunary maximal functions

@article{AndreasSeeger2011,
abstract = {We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H¹ to $L^\{1,∞\}$ bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an $L^p$ regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L² boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally we prove an $L^p$ regularity result for such averages. We formulate various open problems.},
author = {Andreas Seeger, James Wright},
journal = {Banach Center Publications},
keywords = {maximal functions; regularity; measures},
language = {eng},
number = {1},
pages = {235-250},
title = {Problems on averages and lacunary maximal functions},
url = {http://eudml.org/doc/281939},
volume = {95},
year = {2011},
}

TY - JOUR
AU - Andreas Seeger
AU - James Wright
TI - Problems on averages and lacunary maximal functions
JO - Banach Center Publications
PY - 2011
VL - 95
IS - 1
SP - 235
EP - 250
AB - We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H¹ to $L^{1,∞}$ bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an $L^p$ regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L² boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally we prove an $L^p$ regularity result for such averages. We formulate various open problems.
LA - eng
KW - maximal functions; regularity; measures
UR - http://eudml.org/doc/281939
ER -