WEIGHTED ESTIMATES FOR ROUGH PARAMETRIC MARCINKIEWICZ INTEGRALS

Title & Authors
WEIGHTED ESTIMATES FOR ROUGH PARAMETRIC MARCINKIEWICZ INTEGRALS
Al-Qassem, Hussain Mohammed;

Abstract
We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators $\small{\mathcal{M}^{\rho}_{\Omega}}$. As an application of this inequality, we obtain weighted $\small{L^p}$ inequalities for a class of parametric Marcinkiewicz integral operators $\small{\mathcal{M}^{*,\rho}_{\Omega,\lambda}\;and\;\mathcal{M}^{\rho}_{\Omega,S}}$ related to the Littlewood-Paley $\small{g^*_{\lambda}-function}$ and the area integral S, respectively.
Keywords
Marcinkiewicz integral;Littlewood-Paley g-function;Lusin area integral;rough kernel;
Language
English
Cited by
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