Function Theory of Several Complex Variables Book

	Preface to the Second Edition
	Preface to the First Edition
	An Introduction to the Subject	1
1	Some Integral Formulas	19
1.1	The Bochner-Martinelli Formula	19
1.2	Applications of Cauchy Theory and the [actual symbol not reproducible] Equation	31
1.3	Basic Properties of Harmonic Functions	35
1.4	The Bergman Kernel	49
1.5	The Szego and Poisson-Szego Kernels	66
1.6	Afterword to Chapter 1	69
2	Subharmonicity and Its Applications	81
2.1	Subharmonic Functions	81
2.2	Pluriharmonic and Plurisubharmonic Functions	94
2.3	Power Series	99
2.4	Hartogs's Theorem on Separate Analyticity	107
3	Convexity	117
3.1	Many Notions of Convexity	117
3.2	Convexity and Pseudoconvexity	132
3.3	Pseudoconvexity, Plurisubharmonicity, and Analytic Discs	142
3.4	Domains of Holomorphy	151
3.5	Examples of Domains of Holomorphy and the Edge-of-the-Wedge Theorem	159
4	Hormander's Solution of the [actual symbol not reproducible] Equation	175
4.1	Generalities about the [actual symbol not reproducible] Problem	175
4.2	Unbounded Operators on a Hilbert Space	176
4.3	The Formalism of the [actual symbol not reproducible] Problem	179
4.4	Some Computations	182
4.5	An Existence Theorem for the [actual symbol not reproducible] Operator	190
4.6	A Regularity Theorem for the [actual symbol not reproducible] Operator	194
5	Solution of the Levi Problem and Other Applications of [actual symbol not reproducible] Techniques	213
5.1	An Extension Problem	213
5.2	Singular Functions on Strongly Pseudoconvex Domains	216
5.3	Hefer's Lemma and Henkin's Integral Representation	223
5.4	Approximation Problems	228
6	Cousin Problems, Cohomology, and Sheaves	243
6.1	Cousin Problems	243
6.2	Sheaves	254
6.3	Dolbeault Isomorphism	268
6.4	Algebraic Properties of the Ring of Germs of Holomorphic Functions	275
6.5	Sheaf of Divisors, Chern Classes, and the Obstruction to Solving Cousin II	281
7	The Zero Set of a Holomorphic Function	293
7.1	Coherent Analytic Sheaves	293
7.2	Applications of the Cartan and Oka Theorems: The Structure of Ideals	295
7.3	Zeros of One Holomorphic Function	298
7.4	Zero Sets for Different H[superscript p] Spaces Are Different	302
7.5	Zero Sets of H[superscript p] Functions Do Not Have a Simple Mass Distribution Characterization	307
8	Some Harmonic Analysis	321
8.1	Review of the Classical Theory of H[superscript p] Spaces on the Disc	321
8.2	Three Propositions about the Poisson Kernel	330
8.3	Subharmonicity, Harmonic Majorants, and Boundary Values	338
8.4	Pointwise Convergence for Harmonic Functions on Domains in R[superscript N]	344
8.5	Boundary Values of Holomorphic Functions in C[superscript n]	346
8.6	Admissible Convergence	352
8.7	The Lindelof Principle	362
8.8	Additional Tangential Phenomena: Lipschitz Spaces	365
9	Constructive Methods	381
9.1	Story of the Inner Functions Problem	381
9.2	The Hakim/Low/Sibony Construction of Inner Functions	385
9.3	Further Results Obtained with Constructive Methods	395
10	Integral Formulas for Solutions to the [actual symbol not reproducible] Problem and Norm Estimates	403
10.1	The Henkin Integral Formula	403
10.2	Estimates for the Henkin Solution on Domains in C[superscript 2]	407
10.3	Smoothness of the Henkin Solution and the Case Arbitrary [actual symbol not reproducible]-Closed Forms	411
10.4	First Cousin Problem with Bounds and Uniform Approximation on Strongly Pseudoconvex Domains in C[superscript 2]	418
11	Holomorphic Mappings and Invariant Metrics	429
11.1	Classical Theory of Holomorphic Mappings	429
11.2	Invariant Metrics	434
11.3	The Theorem of Bun Wong and Rosay	443
11.4	Smoothness to the Boundary of Biholomorphic Mappings	453
11.5	Concept of Finite Type	462
11.6	Complex Analytic Dynamics	476
App. I	Manifolds	493
App. II	Area Measures	495
App. III	Exterior Algebra	499
App. IV	Vectors, Covectors, and Differential Forms	503
	List of Notation	509
	Bibliography	515
	Index	553