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.

中文翻译：

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广义有界变分函数空间的 $$K$$ -Functional 的双边估计

摘要

对\((C[0,1], BV(X))\)对的\(K\)泛函提出了双边估计，其中\(BV(X)\)是从对称序列空间\(X\)构造的广义有界变分函数。将该估计应用于各种序列空间\(X\)为有限 Wiener-Young \(h\)变体、有限 Waterman \(\Lambda\)变体、有界变分模量的空间产生了新的插值定理Chanturiya等意义上的