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The Dirichlet Space and Related Function Spaces
About this Title
Nicola Arcozzi, University of Bologna, Bologna, Italy, Richard Rochberg, Washington University in Saint Louis, Saint Louis, MO, Eric T. Sawyer, McMaster University, Hamilton, ON, Canada and Brett D. Wick, Washington University in Saint Louis, Saint Louis, MO
Publication: Mathematical Surveys and Monographs
Publication Year:
2019; Volume 239
ISBNs: 978-1-4704-5082-3 (print); 978-1-4704-5360-2 (online)
DOI: https://doi.org/10.1090/surv/239
MathSciNet review: 3969961
MSC: Primary 31-02; Secondary 30-02, 30Hxx, 32-02, 39-02, 47-02
Table of Contents
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Front/Back Matter
The Dirichlet space; Foundations
- Geometry and analysis on the disk
- Hilbert spaces of holomorphic functions
- Intermezzo: Hardy spaces
- Carleson measures
- Analysis on trees
- The Pick property
- Interpolation
The Dirichlet space; Selected topics
- Onto interpolation
- Boundary values
- Alternative norms and applications
- Shift operators and invariant subspaces
- Invariant subspaces of the Dirichlet shift
- Bilinear forms on $\mathcal {D}$
Besov spaces on the ball
- Besov spaces on balls and trees
- Interpolating sequences
- Spaces on trees
- Corona theorems for Besov spaces in $\mathbb {C}^n$
- Some functional analysis
- Schur’s test
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