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

By Șerban Costea, Eric T. Sawyer, Brett D. Wick. 2008

70 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/87801e31382bc5f9c5206f84c2da492f6ca085c1

Citations in the corpus

• Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients (2013, unknown): “Bd // replacing Md for all 1 < p <1 and 0 (see [43]).”