Several Complex Variables and Integral Formulas Book

Preface     vii
Pseudoconvexity and Plurisubharmonicity     1
The Hartogs Theorem     1
Characterizations of Pseudoconvexity     19
The a Problem in Pseudoconvex Domains     47
The Weighted L[superscript 2] Space     47
L[superscript 2] Estimates in Pseudoconvex Domains     53
The Ohsawa-Takegoshi Extension Theorem     100
Integral Formulas for Strictly Pseudoconvex Domains     117
The Homotopy Formula     117
Holder Estimates for the a Problem     143
Bounded and Continuous Extensions     152
H[superscript p] and C[superscript k] Extensions     183
The Bergman Kernel     196
Fefferman's Mapping Theorem     210
Integral Formulas with Weight Factors     245
The Berndtsson-Andersson Formula     245
L[superscript p] Estimates for the a Problem     255
The Berndtsson Formula     264
Counterexamples for L[superscript p] (p > 2) Extensions     270
Bounded Extensions by Means of the Berndtsson Formula     281
The Classical Theory in Several Complex Variables     291
The Poincare Theorem     291
The Weierstrass Preparation Theorem     298
Oka's Fundamental Theorem     307
The Cousin Problem     326
A Compact Operators     331
B Solutions to the Exercises     343
Bibliography     359
Index     365