J. Korean Math. Soc. 2007; 44(6): 1255-1266
Printed November 1, 2007
Copyright © The Korean Mathematical Society.
Hussain Mohammed Al-Qassem
Qatar University
We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators ${\mathcal M}_{\Omega}^{\rho }$. As an application of this inequality, we obtain weighted $L^{p}$ inequalities for a class of parametric Marcinkiewicz integral operators ${\mathcal M}_{\Omega ,\lambda }^{\ast ,\rho }$ and ${\mathcal M}_{\Omega ,S}^{\rho }$ related to the Littlewood-Paley $g_{\lambda }^{\ast }$-function and the area integral $S$, respectively.
Keywords: Marcinkiewicz integral, Littlewood-Paley $g$-function, Lusin area integral, rough kernel
MSC numbers: Primary 42B25
2006; 43(3): 635-658
2005; 42(3): 405-434
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2007; 44(3): 733-745
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