Norm convolution inequalities in lebesgue spaces

Erlan Nursultanov, Sergey Tikhonov, Nazerke Tleukhanova

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    1 Citation (Scopus)

    Abstract

    © European Mathematical Society. We obtain upper and similar lower estimates of the (Lp,Lq) norm for the convolution operator. The upper estimate improves on known convolution inequalities. The technique to obtain lower estimates is applied to study boundedness problems for oscillatory integrals.
    Original languageEnglish
    Pages (from-to)811-838
    JournalRevista Matematica Iberoamericana
    Volume34
    Issue number2
    DOIs
    Publication statusPublished - 1 Jan 2018

    Keywords

    • Convolution
    • Oscillatory kernels
    • Young–O’Neil inequality

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  • Cite this

    Nursultanov, E., Tikhonov, S., & Tleukhanova, N. (2018). Norm convolution inequalities in lebesgue spaces. Revista Matematica Iberoamericana, 34(2), 811-838. https://doi.org/10.4171/rmi/1004