Hardy–Littlewood and Pitt's inequalities for Hausdorff operators

M. Dyachenko, E. Nursultanov, S. Tikhonov

    Research output: Contribution to journalArticleResearchpeer-review

    2 Citations (Scopus)

    Abstract

    © 2018 Elsevier Masson SAS In this paper we study transformed trigonometric series with Hausdorff averages of Fourier coefficients. We prove Hardy–Littlewood and Pitt's inequalities for such series. The corresponding results for the Hausdorff averages of the Fourier transforms are also obtained.
    Original languageEnglish
    Pages (from-to)40-57
    JournalBulletin des Sciences Mathematiques
    Volume147
    DOIs
    Publication statusPublished - 1 Sep 2018

    Keywords

    • Fourier coefficients
    • Hardy–Littlewood theorem
    • Hausdorff operators
    • Pitt's inequality

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