Analysis & PDE
- Anal. PDE
- Volume 4, Number 4 (2011), 499-550.
The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in $\C^n$
We prove that the multiplier algebra of the Drury–Arveson Hardy space on the unit ball in has no corona in its maximal ideal space, thus generalizing the corona theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach space result: the Besov–Sobolev space has the “baby corona property” for all and . In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.
Anal. PDE, Volume 4, Number 4 (2011), 499-550.
Received: 10 March 2010
Revised: 25 May 2010
Accepted: 23 June 2010
First available in Project Euclid: 20 December 2017
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Costea, Şerban; Sawyer, Eric; Wick, Brett. The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in $\C^n$. Anal. PDE 4 (2011), no. 4, 499--550. doi:10.2140/apde.2011.4.499. https://projecteuclid.org/euclid.apde/1513731167
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