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 (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment.
Steven G. Krantz, Washington University, St. Louis, MO.
Chapters Chapter 0. An introduction to the subject Chapter 1. Some integral formulas Chapter 2. Subharmonicity and its applications Chapter 3. Convexity Chapter 4. Hörmander’s solution of the equation Chapter 5. Solution of the Levi problem and other applications of techniques Chapter 6. Cousin problems, cohomology, and sheaves Chapter 7. The zero set of a holomorphic function Chapter 8. Some harmonic analysis Chapter 9. Constructive methods Chapter 10. Integral formulas for solutions to the problem and norm estimates Chapter 11. Holomorphic mappings and invariant metrics Appendix I. Manifolds Appendix II. Area measures Appendix III. Exterior algebra Appendix IV. Vectors, covectors, and differential forms