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SCHAUDER¡¯S ESTIMATE FOR NONLOCAL KINETIC EQUATIONS AND ITS APPLICATIONS

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In this work we develop a new method based on Littlewood-Paley¡¯s decomposition and heat kernel estimates of integral form, to establish Schauder¡¯s estimate for a degenerate nonlocal equation in $mR^{2d}$ with H"older coefficients.As an application, we show the strong well-posedness to the related degenerate stochastic differential equation with H"older drift.