manuscripta mathematica

, Volume 24, Issue 4, pp 351–378 | Cite as

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

  • Steven G. Krantz
Article

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.

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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Steven G. Krantz
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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