On Lp-Generalization of a Theorem of Adamyan, Arov, and Kreın Original Research Article

The paper deals with problems relating to the theory of Hankel operators. Let G be a bounded simple connected domain with the boundary Γ consisting of a closed analytic Jordan curve. Denote by Mn,p(G), 1⩽p<∞, the class of all meromorphic functions on G that can be represented in the form h=β/α, where β belongs to the Smirnov class Ep(G), α is a polynomial degree at most n, α≢0. We obtain estimates of s-numbers of the Hankel operator Af constructed from f∈Lp(Γ), 1⩽p<∞, in terms of the best approximation Δn,p of f in the space Lp(Γ) by functions belonging to the class Mn,p(G).