• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1923-1936
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• 2013

We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^*_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by BMO functions are also considered.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1255-1266
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• 2007

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