Smoothness of functions and Fourier coefficients

M. I. Dyachenko, A. B. Mukanov, S. Yu Tikhonov

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    1 Citation (Scopus)

    Abstract

    © 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the Lp modulus of smoothness, 1 < p < ∞, of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory.
    Original languageEnglish
    Pages (from-to)994-1018
    Number of pages25
    JournalSbornik Mathematics
    Volume210
    Issue number7
    DOIs
    Publication statusPublished - Jul 2019

    Keywords

    • CONTINUITY
    • Fourier series
    • L-P
    • MODULI
    • MONOTONICITY
    • TRANSFORMS
    • TRIGONOMETRIC SERIES
    • general monotone sequences
    • moduli of smoothness

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