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Full-Text Articles in Physical Sciences and Mathematics
Maximal Oscillatory Singular Integrals With Kernels In L Log L(S^{N-1}), Ahmad Al-Salman
Maximal Oscillatory Singular Integrals With Kernels In L Log L(S^{N-1}), Ahmad Al-Salman
Turkish Journal of Mathematics
In this paper, we study the L^p mapping properties of a certain class of maximal oscillatory singular integral operators. We establish the L^p boundedness of our operators provided that their kernels belong to the natural space L log ^+L(S^{n-1}). Our result substantially improves a previously known result. Moreover, the approach developed in this paper can be applied to handle more general maximal oscillatory singular integral operators.
On Marcinkiewicz Integrals Along Flat Surfaces, Ahmad Al-Salman
On Marcinkiewicz Integrals Along Flat Surfaces, Ahmad Al-Salman
Turkish Journal of Mathematics
In this paper, we study Marcinkiewicz integral operators with rough kernels supported by surfaces given by flat curves. Under convexity assumptions on our surfaces, we establish an L^p boundedness result of such operators. Moreover, we obtain the L^p boundedness of the corresponding Marcinkiewicz integral operators that are related to area integral and Littlewood-Paley g_{\lambda}^* functions.