Two-sided estimates of the $K$-functional for spaces of functions of generalized bounded variation

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.