On Marcinkiewicz Integrals along flat surfaces


Abstract: 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.

Keywords: Marcinkiewicz integral, rough kernels, flat curves, Fourier transform, area integral, Littlewood-Paley g_{\lambda}^* functions

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