Lp Estimates of certain rough parametric Marcinkiewicz functions
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DOI: 10.1007/s11464-019-0792-6
Abstract: We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the \(L^1(\mathbb{S}^{n-1})\) integrability condition. The obtained Lp estimates resolve a problem left open in previous work. Our argument… read more here.
Keywords: parametric marcinkiewicz; rough parametric; certain rough; estimates certain ... See more keywords
On Rough Parametric Marcinkiewicz Integrals Along Certain Surfaces
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DOI: 10.3390/math13081287
Abstract: In this paper, we study rough Marcinkiewicz integrals associated with surfaces defined by ΨP,ϕ={(˜P(w),ϕ(w)):w∈Rm}. We establish the Lp-boundedness of these integrals when the kernel functions lie in the Lq(Sm−1) space. Combining this result with Yano’s… read more here.
Keywords: along certain; integrals along; parametric marcinkiewicz; marcinkiewicz integrals ... See more keywords
Inequalities for generalized parametric Marcinkiewicz integrals along polynomial compound curves
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DOI: 10.7153/jmi-2020-14-14
Abstract: Under some weaker size conditions assumed on the integral kernels both on the unit sphere and in the radial directions, the sharp Lp boundedness was proved for the generalized parametric Marcinkiewicz integrals along polynomial compound… read more here.
Keywords: parametric marcinkiewicz; integrals along; generalized parametric; marcinkiewicz integrals ... See more keywords