THE CORONA THEOREM FOR THE DRURY-ARVESON HARDY SPACE AND OTHER HOLOMORPHIC BESOV-SOBOLEV SPACES ON THE UNIT BALL IN C-n

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.


Published in:
Analysis & Pde, 4, 499-550
Year:
2011
Keywords:
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 Record created 2012-06-25, last modified 2018-01-28


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