Costea, SerbanSawyer, Eric T.Wick, Brett D.2012-06-252012-06-252012-06-25201110.2140/apde.2011.4.499https://infoscience.epfl.ch/handle/20.500.14299/82189WOS:000299676200001We 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.enBesov-Sobolev Spacescorona Theoremseveral complex variablesToeplitz corona theoremStrictly Pseudoconvex DomainsKernel Hilbert-SpacesMultipliersInterpolationPolydiskThe corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in C-ntext::journal::journal article::research article