On Approximation Of Functions In The Spaces L_p(r~2) And L_p(r_+~2)by Generalized Singular Integrals With Positive Kernels

摘要

The following question is discussed: How the behavior of ‖∫_(F~2)Δ_(u,v)~r(f;·)φ_n(u)φ_m(v)dudv‖_(p,R~2) as n, m → ∞, where F is contained in R, Δ_(u,v)~r(f;x,y)=∑_(i,j=1)~r(-1)~(r-j)C_r~jC_r~jf(x+ju,y+jv)-f(x,y), ψ_n and ψ_m are positive kernels, is connected with the structural properties of f that are characterized by the moduli of continuity? Bibliography: 2 titles.