The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in ℂn Academic Article uri icon

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abstract

  • 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

publication date

  • January 1, 2011