On maximal functions with rough kernels in L (log L)1/2(Sn-1).

Al-Salman, Ahmad. "On maximal functions with rough kernels in L (log L)1/2(Sn-1).." Collectanea Mathematica 56.1 (2005): 47-56. <http://eudml.org/doc/41820>.

@article{Al2005,
abstract = {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.},
author = {Al-Salman, Ahmad},
journal = {Collectanea Mathematica},
keywords = {singular integrals; maximal operator; Marcinkiewicz integral; boundedness},
language = {eng},
number = {1},
pages = {47-56},
title = {On maximal functions with rough kernels in L (log L)1/2(Sn-1).},
url = {http://eudml.org/doc/41820},
volume = {56},
year = {2005},
}

TY - JOUR
AU - Al-Salman, Ahmad
TI - On maximal functions with rough kernels in L (log L)1/2(Sn-1).
JO - Collectanea Mathematica
PY - 2005
VL - 56
IS - 1
SP - 47
EP - 56
AB - 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.
LA - eng
KW - singular integrals; maximal operator; Marcinkiewicz integral; boundedness
UR - http://eudml.org/doc/41820
ER -