The Corona Theorem for the Drury-Arveson Hardy space and other holomorphic Besov-Sobolev spaces on the unit ball in $\mathbb{C}^{n}$

Details The Corona Theorem for the Drury-Arveson Hardy space and other holomorphic Besov-Sobolev spaces on the unit ball in $\mathbb{C}^{n}$ The Corona Theorem for the Drury-Arveson Hardy space and other holomorphic Besov-Sobolev spaces on the unit ball in $\mathbb{C}^{n}$

2008-11-04

arxiv.org/abs/0811.0627v7

Anal. PDE 4 (2011), no. 4, 499--550

Mathematics

Complex Variables

v1: 70 pgs; v2: 73 pgs.; introduction expanded, clarified. v3: 73 pgs.; restriction in main result removed (see 9.2), argument

Scientific paper

10.2140/apde.2011.4.499

We prove that the multiplier algebra of the Drury-Arveson Hardy space $H_{n}^{2}$ on the unit ball in $\mathbb{C}^{n}$ has no corona in its maximal ideal space, thus generalizing the famous 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 $B_{p}^{\sigma}$ has the "baby corona property" for all $\sigma \geq 0$ and $1

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