Abstract
Sharp tangential Lipschitz estimates for the inhomogeneous Cauchy Riemann equations with Lp 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.
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This work was partially supported by NSF Grant # MCB 77-02213
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Krantz, S.G. Estimates for integral kernels of mixed type, fractional integration operators, and optimal estimates for the\(\bar \partial \) operator. Manuscripta Math 30, 21–52 (1979). https://doi.org/10.1007/BF01305989
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DOI: https://doi.org/10.1007/BF01305989