Estimates for integral kernels of mixed type,fractional integration operators,and optimal estimates for thebar partial operator

Sharp tangential Lipschitz estimates for the inhomogeneous Cauchy Riemann equations with L^p data on strongly pseudoconvex doma ins in complex manifolds are proved. Estimates in both isotropic and non-isotropic spaces of functions of bounded mean oscillation are proved.Tangential estimates for a large class of domains are shown to follow from those on the ball.In the course of the proofs a fractional integration theorem of independent interest is proved.This work was partially supported by NSF Grant # MCB 77-02213