广义有界变分函数空间\(K\)泛函的双面估计

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI:10.1134/S0016266322010026

E. I. Berezhnoi

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引用次数: 0

摘要

提出了对\((C[0,1], BV(X))\)的\(K\) -泛函的双边估计，其中\(BV(X)\)是由对称序列空间\(X\)构造的广义有界变分函数空间。将这一估计应用于各种序列空间\(X\)，得到了有限Wiener-Young \(h\) -变分空间、有限Waterman \(\Lambda\) -变分空间、Chanturiya意义上的有限变分模等新的插值定理。

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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.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.