On estimates of diameter values of classes of functions in the weight space L2,γ (ℝ2), γ = exp(–x2 – y2)

Abstract

For a function f ∈ L2,γ (R 2 ), the q-averaging of the generalized m-order modulus of continuity Ωm,γ (f ) with the weight function ϕ, i.e., the value of Mq(Ωm,γ (f ), ϕ; t) (t ∈ (0, 1); m ∈ N; q ∈ (0, ∞)) has been considered. With its help and with the participation of the majorant Ψ, classes of two-variable functions W2(Ω q m,γ , ϕ;∀t ∈ (0, 1)} were introduced, for which upper and lower estimates of various diameters in the space L2,γ (R 2 ) were found. A certain condition on the majorant Ψ was found, under which exact diameter values can be calculated. A similar problem has been considered for the classes W r,0 2 (Ω q m,γ , ϕ;A number of results related to the specification of the exact values of various diameters are given.