Journal
ANALYSIS & PDE
Volume 4, Issue 4, Pages 499-550Publisher
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/apde.2011.4.499
Keywords
Besov-Sobolev Spaces; corona Theorem; several complex variables; Toeplitz corona theorem
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Funding
- National Science and Engineering Research Council of Canada
- National Science Foundation DMS [0752703]
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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.
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