abstract
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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
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