**Fields Institute Monographs**

Volume: 25;
2009;
203 pp;
Hardcover

MSC: Primary 30; 32;
Secondary 42; 46

Print ISBN: 978-0-8218-4734-3

Product Code: FIM/25

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-1-4704-1788-8
Product Code: FIM/25.E**

List Price: $69.00

Individual Member Price: $55.20

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#### Supplemental Materials

# Function Theory: Interpolation and Corona Problems

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*Eric T. Sawyer*

A co-publication of the AMS and Fields Institute

These lecture notes take the reader from Lennart Carleson's first deep results on interpolation and corona problems in the unit disk to modern analogues in the disk and ball. The emphasis is on introducing the diverse array of techniques needed to attack these problems rather than producing an encyclopedic summary of achievements. Techniques from classical analysis and operator theory include duality, Blaschke product constructions, purely Hilbert space arguments, bounded mean oscillation, best approximation, boundedness of the Beurling transform, estimates on solutions to the \(\bar\partial\) equation, the Koszul complex, use of trees, the complete Pick property, and the Toeplitz corona theorem. An extensive appendix on background material in functional analysis and function theory on the disk is included for the reader's convenience.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## Function Theory: Interpolation and Corona Problems

- Cover Cover11
- Title page iii5
- Contents v7
- Preface vii9
- Preliminaries 113
- The interpolation problem 921
- The corona problem 3547
- Toeplitz and Hankel operators 5567
- Hilbert function spaces and Nevanlinna-Pick kernels 8799
- Carleson measures for the Hardy-Sobolev spaces 133145
- Functional analysis 145157
- Weak derivatives and Sobolev spaces 173185
- Function theory on the disk 183195
- Spectral theory for normal operators 195207
- Bibliography 199211
- Index 201213
- Back Cover Back Cover1219

#### Readership

Graduate students and research mathematicians interested in function theory in the unit disk and ball, and interpoloation and corona problems.