On Blaschke products associated with n-widths

Abstract

Let E be a closed subset of the open unit disk G={z : |z|<1} , and let μ be a positive Borel measure with support supp μ= E. Denote by A p the restriction on E of the closed unit ball of the Hardy space H p ( G), 1⩽ p⩽∞. In this paper we investigate orthogonality properties of the extremal functions associated with the Kolmogorov, Gelfand, and linear n-widths of A p in L q ( μ, E), 1⩽ q<∞, q⩽ p.