There has been a flurry of activity in recent years in the loosely
defined area of holomorphic spaces. This book discusses the most
well-known and widely used spaces of holomorphic functions in the
unit ball of Cn. Spaces discussed include the Bergman spaces, the
Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov
spaces, and the Lipschitz spaces. Most proofs in the book are new
and simpler than the existing ones in the literature. The central
idea in almost all these proofs is based on integral
representations of holomorphic functions and elementary properties
of the Bergman kernel, the Bergman metric, and the automorphism
group.
The unit ball was chosen as the setting since most results can
be achieved there using straightforward formulas without much fuss.
The book can be read comfortably by anyone familiar with single
variable complex analysis; no prerequisite on several complex
variables is required. The author has included exercises at the end
of each chapter that vary greatly in the level of difficulty.
General
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