Publication

The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in C-n

Serban Mihai Costea
2011
Journal Articles

Abstract

We prove that the multiplier algebra of the Drury-Arveson Hardy space H-n(2) on the unit ball in C-n 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 B-p(sigma) has the "baby corona property" for all sigma >= 0 and 1 < p < infinity. In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.

Official source

https://infoscience.epfl.ch/entities/publication/f3cd7cb5-9749-4a8e-8584-9d58d2d39d2e

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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-n

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