The Corona Problem, Carleson Measures, and Applications

Carleson measures were introduced by Lennart Carleson in 1962 to solve an interpolation problem about bounded holomorphic function called the corona problem. Since then Carleson measures have been both a powerful tool and a mathematical object worth of study per se and research on the corona problem...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical Analysis and Applications S. 709 - 730
1. Verfasser: Saracco, Alberto
Format: Buchkapitel
Sprache:Englisch
Veröffentlicht: United States John Wiley & Sons, Incorporated 2018
John Wiley & Sons, Inc
Schlagworte:
Banach algebras
bounded holomorphic functions
Carleson measures
complex variable
corona problem
hypercomplex variable
ISBN:9781119414346, 1119414342
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Carleson measures were introduced by Lennart Carleson in 1962 to solve an interpolation problem about bounded holomorphic function called the corona problem. Since then Carleson measures have been both a powerful tool and a mathematical object worth of study per se and research on the corona problem or Carleson measures has gone a long way in the last 50 years. In this chapter, we will review the developments and generalizations of the corona problem, the results on Carleson measures themselves and some applications of Carleson measures, in several different settings, starting from the disc in C (where the corona problem was originally set) arriving to the unit ball in C n , to bounded strongly pseudoconvex domains and even to domains in the quaternionic space. Both the corona problem and the Carleson measures still need investigation, as many open problems have not been solved yet. The open problems are highlighted with a bold font, for the reader's convenience.
ISBN:9781119414346
1119414342
DOI:10.1002/9781119414421.ch20