eBookISBN:  9781470413651 
Product Code:  SURV/138.E 
List Price:  $97.00 
MAA Member Price:  $87.30 
AMS Member Price:  $77.60 
eBook ISBN:  9781470413651 
Product Code:  SURV/138.E 
List Price:  $97.00 
MAA Member Price:  $87.30 
AMS Member Price:  $77.60 

Book DetailsMathematical Surveys and MonographsVolume: 138; 2007; 348 ppMSC: Primary 47; 30; 46; 32;
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes.
Most results concern the relationship between operatortheoretic properties of these operators and functiontheoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study.
The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems.
Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.ReadershipGraduate students and research mathematicians interested in complex analysis and operator theory.

Table of Contents

Chapters

1. Bounded linear operators

2. Interpolation of Banach spaces

3. Integral operators on $L^p$ spaces

4. Bergman spaces

5. Bloch and Besov spaces

6. The Berezin transform

7. Toeplitz operators on the Bergman space

8. Hankel operators on the Bergman space

9. Hardy spaces and BMO

10. Hankel operators on the Hardy space

11. Composition operators


Additional Material

Reviews

...the present title definitely has become a classic in the area. This highly welcome updated, revised, and enlarged new edition of Zhu's book has every chance of maintaining the book's position as one of the standard references in the area.
Mathematical Reviews 
Overall, providing current major developments in operator theoretic function theory in a clear and unified way, this new edition appears to be a significant contribution to the field and will be of value to both active researchers and advanced graduate students.
Zentralblatt MATH


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This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes.
Most results concern the relationship between operatortheoretic properties of these operators and functiontheoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study.
The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems.
Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Graduate students and research mathematicians interested in complex analysis and operator theory.

Chapters

1. Bounded linear operators

2. Interpolation of Banach spaces

3. Integral operators on $L^p$ spaces

4. Bergman spaces

5. Bloch and Besov spaces

6. The Berezin transform

7. Toeplitz operators on the Bergman space

8. Hankel operators on the Bergman space

9. Hardy spaces and BMO

10. Hankel operators on the Hardy space

11. Composition operators

...the present title definitely has become a classic in the area. This highly welcome updated, revised, and enlarged new edition of Zhu's book has every chance of maintaining the book's position as one of the standard references in the area.
Mathematical Reviews 
Overall, providing current major developments in operator theoretic function theory in a clear and unified way, this new edition appears to be a significant contribution to the field and will be of value to both active researchers and advanced graduate students.
Zentralblatt MATH