In this paper, we study the Lp mapping properties of maximal functions with rough kernels that are related to certain class of singular integral operators. We prove that our maximal functions are bounded on Lp provided that their kernels are in L (log L)1/2(Sn-1). Moreover, we present an example showing that our size condition on the kernel is optimal. As a consequence of our result, we substantially improve previously known results on maximal functions, singular integral operators, and Parametric Marcinkiewicz integral operators.
@article{urn:eudml:doc:41820,
title = {On maximal functions with rough kernels in L (log L)1/2(Sn-1).},
journal = {Collectanea Mathematica},
volume = {56},
year = {2005},
pages = {47-56},
zbl = {1086.42008},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41820}
}
Al-Salman, Ahmad. On maximal functions with rough kernels in L (log L)1/2(Sn-1).. Collectanea Mathematica, Tome 56 (2005) pp. 47-56. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41820/