Approximation of differentiation operators by bounded linear operators in Lebesgue spaces on the axis and related problems in the spaces of \((p,q)\)-multipliers and their predual spaces
In this article best approximations and operators that provide these best approximations are studied. The functions that are being approximated are univariate and are of certain smoothness classes, their derivatives being locally absolutely continuous and in some \(L^p\)-space.\N\NFor some given positive \(N\) we consider all operators \(T\) between such spaces with operator norm at most \(N\). We then look for the bounded linear operator(s) that give(s) the least error \(U(T)\) approximating a derivative of an approximand by the operator applied to functions whose \(n\)-derivatives have at lost \(L_p\)-norm one.\N\NThis is a Stechkin-type problem, and the paper provides solutions for this in some special cases.
predual space for space of \((p, q)\)-multipliers
scientific article; zbMATH DE number 7882015
scientific article