Hardy-type theorems on Fourier transforms revised

M. Dyachenko, E. Nursultanov, S. Tikhonov

    Research output: Contribution to journalArticleResearch

    Abstract

    © 2018 Elsevier Inc. We obtain new conditions on periodic integrable functions so that their transformed Fourier series belong to Lp. This improves the classical Hardy and Bellman results. A counterpart for the Fourier transforms is also established. Our main tool is a new extension of the Hausdorff–Young–Paley inequality for Fourier transforms.
    Original languageEnglish
    Pages (from-to)171-184
    JournalJournal of Mathematical Analysis and Applications
    Volume467
    DOIs
    Publication statusPublished - 1 Nov 2018

    Keywords

    • Fourier coefficients/transforms
    • Hardy and Hardy–Cesàro averages
    • Hardy–Littlewood theorem
    • Hausdorff–Young–Paley inequality

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