We prove that the multiplier algebra of the Drury-Arveson Hardy space H 2 n on the unit ball in ‫ރ‬ 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 has the "baby corona property" for all 0 and 1 < p < 1. In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.

Abstract. This paper studies the inclusions between different Sobolev-Lorentz spaces W

This paper studies Besov p-capacities as well as their relationship to Hausdorff measures in Ahlfors regular metric spaces of dimension Q for 1 < Q < p < ∞. Lower estimates of the Besov p-capacities are obtained in terms of the Hausdorff content associated with gauge functions h satisfying the decay condition

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