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14 edition of Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics) found in the catalog.

# Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics)

## by Kehe Zhu

Written in English

The Physical Object
Number of Pages268
ID Numbers
Open LibraryOL7444395M
ISBN 100387220364
ISBN 109780387220369

Could you please give me some examples of Hilbert spaces of holomorphic functions? Or even books or notes on Hilbert spaces of holomorphic functions? I need just a good number of examples and perhaps some general properties. Thanks in advance! G. Popescu / Journal of Functional Analysis () – regarded as the boundary function of the Poisson extension P[A].Using some results from [29, 30,34], we characterize the free holomorphic functions u on the open unit ball [B(H)n]1 such that u=P[f] for some boundary function f in the noncommutative analytic Toeplitz algebra F∞.

Spaces of holomorphic functions on the unit disk D of the complex plane play an important role in mathematical analysis, and the study of such spaces naturally con- nects complex and harmonic.   Categories: E-Books & Audio Books Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics, Vol. ) pages | English | ISBN | ISBN

OPERATORS BETWEEN BLOCH/LIPSCHITZ SPACES OF THE UNIT BALL DANA D. CLAHANE AND STEVO STEVIC´ Abstract. For p > 0, let Bp(Bn) and Lp(Bn) respectively denote the p-Bloch and holomorphic p-Lipschitz spaces of the open unit ball Bn in Cn. It is known that Bp(Bn) and L1−p(Bn) are equal as sets when p ∈ (0,1). We prove that these spaces are. Implications of complex structure. Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.. For example, the Whitney embedding theorem tells us that every smooth n-dimensional manifold can be embedded as .

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### Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics) by Kehe Zhu Download PDF EPUB FB2

This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. 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 by:   This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. 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 cturer: Springer. "This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C[superscript n]. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces.

This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. 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. We introduce the F ˜ G (p,q,s) and F ˜ φ (p,q,s) vector spaces of holomorphic functions defined in the unit ball of ℂ n, generalizing previous work like Ouyang et al.

(), Stroethoff. We introduce the and vector spaces of holomorphic functions defined in the unit ball of, generalizing previous work like Ouyang et al. (), Stroethoff (), and Choa et al. Likewise, we characterize those spaces in terms of harmonic majorants as a generalization of Arellano et al.

The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones.

the basic de nitions. For p>0 the Hardy space Hpconsists of the holomorphic functions fin the unit disk, D, satisfying the growth condition sup0function on the unit circle de ned by fr ei = f rei, and kfrkp denotes the norm of fr in the Lp space of normalized Lebesgue measure on the circle, hereafter denoted.

The study of this space was one of the main motivations for the celebrated theorem of Josefson [40] and Nissenzweig [53]. Section 5 is devoted to the study of the space of bounded holomorphic map-pings. The still unsolved problem as to whether the space of bounded holomor-phic functions on the open unit disc has the approximation property, is.

(Marco M. Peloso, Mathematical Reviews, Issue d)"The book is concerned with the basic properties of the most well-known and widely used spaces in holomorphic functions in the open unit ball Bn of Cn. The restriction to the unit ball of Cn allows the author to present direct proofs of most of the results by straightforward formulas.

(Marco M. Peloso, Mathematical Reviews, Issue d) "The book is concerned with the basic properties of the most well-known and widely used spaces in holomorphic functions in the open unit ball Bn of Cn.

The restriction to the unit ball of Cn allows the author to present direct proofs of most of the results by straightforward formulas. The book is well written and can be used as a textbook. The open unit ball in Cn is the set B n = {z ∈ Cn: |z| space of all holomorphic functions in B n.

For any −∞. Buy Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics) by Kehe Zhu (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible orders. The Bloch space plays a very important role in classical geometric func-tion theory. The one dimensional case of the holomorphic Bloch space is well investigated. The aim of this paper is the study of the Bloch space on the unit ball in Cn:We give a new generalization of.

Spaces of Holomorphic Functions in the Unit Ball This book is devoted to the study of various spaces of holomorphic functions on the unit ball.

The main tool used for their study is an explicit form of the Bergman and Cauchy-Szëgo kernels. There is a lot of different spaces of that sort and the author has chosen some of them for a detailed study.

Zhu, Spaces of Holomorphic Functions in the Unit Ball, 1st Edition. Softcover version of original hardcover edition, Buch, Bücher schnell und portofrei Beachten Sie bitte die aktuellen Informationen unseres Partners DHL zu Liefereinschränkungen im Ausland.

on the space 0(B) of holomorphic functions on the unit ball. Following [2] we define for each q > 0 a measure dVq on B by dVqiz) = Gnj9(l — ¡z^^^'-dViz), where dV is the usual Lebesgue measure on C™ and the constant CnA is chosen so that dVq is a probability measure on B.

For g>0,0. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. 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 : Kehe Zhu. As outlined below, this paper is devoted to a Carleson-type-measure-based study of the holomorphic Campanato \$2\$-space on the open unit ball \$\mathbb B_n\$ of \$\mathbb C^n\$, comprising all Hardy \$2.

The book has evolved with the teaching/research experience of Professor Zhu at the State University of New York at Albany.

It is not comprehensive, but it includes the most well known spaces of holomorphic functions in the unit ball of C n.

Besov–Lipschitz and Mean Besov–Lipschitz Spaces of Holomorphic Functions on the Unit Ball Article (PDF Available) in Potential Analysis 38(4) May with Reads.A real- or complex-valued function uis harmonic on an open subset of Rn if u 0 on.

The purpose of this article is to present an elementary treat-ment of some known results for the harmonic Bergman spaces consisting of all harmonic functions on the unit ball in Rn that are p .We study two classes of holomorphic functions in the unit ball B n of C n: mean Lipschitz spaces and Hardy Sobolev spaces.

Main results include new characteriza-tions in terms of fractional.