, Volume 24, Issue 4, pp 351-378

Intrinsic Lipschitz classes on manifolds with applications to complex function theory and estimates for the \(\bar \partial \) and \(\bar \partial _b \) equations

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Abstract

An intrinsic definition of Lipschitz classes in terms of vector fields on man-ifolds is provided and it is shown that it is locally equivalent with a more classical definition. A finer result is then proved for strongly pseudo-convex CR manifolds and applications of the theorems are given to smoothness of holomorphic functions and estimates for the \(\bar \partial \) and \(\bar \partial _b \) . equations.