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The corona theorem for
the Drury–Arveson Hardy space and other holomorphic
Besov–Sobolev spaces on the unit ball in $\C^n$
Şerban Costea, Eric T. Sawyer and Brett D. Wick |
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Vol. 4 (2011), No. 4, 499–550
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Abstract |
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We prove that the multiplier algebra of the Drury–Arveson Hardy space on the unit ball in 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 has the “baby corona property” for all and . In addition we obtain infinite generator and semi-infinite matrix versions of these theorems. |
Keywords
Besov–Sobolev Spaces, corona Theorem, several complex
variables, Toeplitz corona theorem
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Mathematical Subject Classification 2000
Primary: 30H05, 32A37
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Supplementary material |
Milestones
Received: 10 March 2010
Revised: 25 May 2010
Accepted: 23 June 2010
Published: 9 January 2012
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Authors |
| Şerban Costea | |
| Department of Mathematics and
Statistics McMaster University 1280 Main Street West Hamilton, ON L8S 4K1 Canada |
École Polytechnique Fédérale de
Lausanne EPFL SB MATHGEOM Station 8 CH-1015 Lausanne Switzerland |
| Eric T. Sawyer | |
| Department of Mathematics and
Statistics McMaster University 1280 Main Street West Hamilton, ON L8S 4K1 Canada |
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| Brett D. Wick | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160 United States |
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