SCHAUDER’S ESTIMATE FOR NONLOCAL KINETIC EQUATIONS AND ITS APPLICATIONS

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.