IJPAM: Volume 15, No. 1 (2004)

ROUGH PARAMETRIC MARCINKIEWICZ FUNCTIONS

Ahmad Al-Salman$^1$, Ali A. Al-Jarrah$^2$
$^{1,2}$Department of Mathematics
Yarmouk University
Irbid, JORDAN
$^1$e-mail: alsalman@yu.edu.jo
$^2$e-mail: alia@yu.edu.jo


Abstract.In this paper, we study the $L^p$ mapping properties of parametric Marcinkiewicz operators introduced by Hörmander. We prove the $L^p$ boundedness of these operators under very weak size conditions on their kernels. Our result substantially improves the result in [#!ho!#].

Received: June 8, 2004

AMS Subject Classification: 42B20, 42B15, 42B25

Key Words and Phrases: parametric Marcinkiewicz operators, rough kernels, Fourier transforms, maximal functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 15
Issue: 1