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The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in ℂ<sup><i>n</i></sup>
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 …