Theory of Bergman Spaces

1. Front Matter

   Pages i-ix

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2. The Bergman Spaces

   • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

   Pages 1-27

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3. The Berezin Transform

   • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

   Pages 28-51

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4. A^p -Inner Functions

   • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

   Pages 52-97

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5. Zero Sets

   • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

   Pages 98-135

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6. Interpolation and Sampling

   • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

   Pages 136-175

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7. Invariant Subspaces

   • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

   Pages 176-189

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8. Cyclicity

   • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

   Pages 190-215

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9. Invertible Noncyclic Functions

   • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

   Pages 216-241

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10. Logarithmically Subharmonic Weights

    • Haakan Hedenmalm, Boris Korenblum, Kehe Zhu

    Pages 242-273

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11. Back Matter

    Pages 274-289

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Preliminary Text. Do not use. 15 years ago the function theory and operator theory connected with the Hardy spaces was well understood (zeros; factorization; interpolation; invariant subspaces; Toeplitz and Hankel operators, etc.). None of the techniques that led to all the information about Hardy spaces worked on their close relatives the Bergman spaces. Most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely. Now the situation has completely changed. Today there are rich theories describing the Bergman spaces and their operators. Research interest and research activity in the area has been high for several years. A book is badly needed on Bergman spaces and the three authors are the right people to write it.

• Function Theory
• Nevanlinna theory
• Operator theory
• algebra
• bounded mean oscillation
• extrema
• logarithm

“Each chapter ends with a section called Notes and another called Exercises and Further Results. … It would be quite suitable for graduate students in the field.” (Lou Zengjian, zbMATH 0955.32003, 2022)

• Department of Mathematics, Lund University, Lund, Sweden

  Haakan Hedenmalm

• Department of Mathematics, State University of New York at Albany, Albany, USA

  Boris Korenblum, Kehe Zhu

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