The corona theorem for the drury-arveson hardy space and other holomorphic Besov-Sobolev spaces on the unit ball in Cⁿ

We prove that the multiplier algebra of the Drury-Arveson Hardy space H²_n on the unit ball in Cⁿ has no corona in its maximal ideal space, thus generalizing the corona theorem of L. Carleson to higher dimensions. This result is obtained asa corollary of the Toeplitz corona theorem and a new Banach space result: the Besov-Sobolev space B^σ_p has the "baby corona property" for all σ ≥ 0 and 1 < p < In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.