Function Theory of Several Complex Variables
This work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory. While due homage is paid to the more traditional algebraic theory (for example, sheaves, and Cousin problems), the student with a background in real and complex variable theory, harmonic analysis, and differential equations should be most comfortable with this treatment.
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Some harmonic analysis
Integral formulas for solutions to the problem and norm estimates
Holomorphic mappings and invariant metrics
Appendix I Manifolds
Appendix II Area measures
Appendix III Exterior algebra
Appendix IV Vectors covectors and differential forms