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

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, P. G. Demidov Yaroslavl’ State University, Yaroslavl, Russia

    E. I. Berezhnoi

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  1. E. I. Berezhnoi
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Correspondence to E. I. Berezhnoi.

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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2022, Vol. 56, pp. 26–36 https://doi.org/10.4213/faa3946.

Translated by O. V. Sipacheva

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Berezhnoi, E.I. Two-Sided Estimates of the \(K\)-Functional for Spaces of Functions of Generalized Bounded Variation. Funct Anal Its Appl 56, 19–26 (2022). https://doi.org/10.1134/S0016266322010026

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  • DOI: https://doi.org/10.1134/S0016266322010026

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