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research article
The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in C-n
2011
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.
Type
research article
Web of Science ID
WOS:000299676200001
Authors
Publication date
2011
Published in
Volume
4
Start page
499
End page
550
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
June 25, 2012
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