manuscripta mathematica

, Volume 24, Issue 4, pp 351-378

First online:

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

  • Steven G. KrantzAffiliated withDepartment of Mathematics, University of California

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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.