03048nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003100137050001200168072001700180072002300197082001500220100002400235245009200259264004600351300003200397336002600429337002600455338003600481347002400517490005300541505014900594520134800743650001702091650002702108650002802135650003602163650001702199650005102216650001402267710003402281773002002315776003602335830005302371856004402424912001402468999001902482952007702501978-0-387-27539-0DE-He21320180115171353.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97803872753909978-0-387-27539-07 a10.1007/0-387-27539-82doi 4aQA331.7 7aPBKD2bicssc 7aMAT0340002bisacsh04a515.942231 aZhu, Kehe.eauthor.10aSpaces of Holomorphic Functions in the Unit Ballh[electronic resource] /cby Kehe Zhu. 1aNew York, NY :bSpringer New York,c2005. aX, 274 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aGraduate Texts in Mathematics,x0072-5285 ;v2260 aPreliminaries -- Bergman Spaces -- The Bloch Space -- Hardy Spaces -- Functions of Bounded Mean Oscillation -- Besov Spaces -- Lipschitz Spaces. aThere 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 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. 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. Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include Operator Theory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springer 2000), and An Introduction to Operator Algebras (CRC Press 1993). 0aMathematics. 0aMathematical analysis. 0aAnalysis (Mathematics). 0aFunctions of complex variables.14aMathematics.24aSeveral Complex Variables and Analytic Spaces.24aAnalysis.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387220369 0aGraduate Texts in Mathematics,x0072-5285 ;v22640uhttp://dx.doi.org/10.1007/0-387-27539-8 aZDB-2-SMA c369325d369325 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK