Two-Sided Estimates of the \(K\)-Functional for Spaces of Functions of Generalized Bounded Variation

Abstract

A two-sided estimate is proposed for the \(K\)-functional of the pair \((C[0,1], BV(X))\), where \(BV(X)\) is the space of functions of generalized bounded variation constructed from a symmetric sequence space \(X\). The application of this estimate to various sequence spaces \(X\) yields new interpolation theorems for spaces of finite Wiener–Young \(h\)-variation, of finite Waterman \(\Lambda\)-variation, of bounded modulus of variation in the sense of Chanturiya, etc.