## 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 $\C^n$

#### Abstract

We prove that the multiplier algebra of the Drury–Arveson Hardy space $Hn2$ on the unit ball in $ℂn$ 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 $Bpσ$ has the “baby corona property” for all $σ≥0$ and $1. In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.

#### Article information

Source
Anal. PDE, Volume 4, Number 4 (2011), 499-550.

Dates
Revised: 25 May 2010
Accepted: 23 June 2010
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513731167

Digital Object Identifier
doi:10.2140/apde.2011.4.499

Mathematical Reviews number (MathSciNet)
MR3077143

Zentralblatt MATH identifier
1264.32004

#### Citation

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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#### Supplemental materials

• PDF file containing proofs of formulas and modifications of arguments already in the literature that would otherwise interrupt the main flow of the paper.