Positive L p -Bounded Dunkl-Type Generalized Translation Operator and Its Applications

D. V. Gorbachev, V. I. Ivanov, S. Yu Tikhonov

    Research output: Contribution to journalArticleResearch

    19 Citations (Scopus)

    Abstract

    © 2018, Springer Science+Business Media, LLC, part of Springer Nature. We prove that the spherical mean value of the Dunkl-type generalized translation operator τ y is a positive L p -bounded generalized translation operator T t . As applications, we prove the Young inequality for a convolution defined by T t , the L p -boundedness of τ y on radial functions for p> 2 , the L p -boundedness of the Riesz potential for the Dunkl transform, and direct and inverse theorems of approximation theory in L p -spaces with the Dunkl weight.
    Original languageEnglish
    Pages (from-to)555-605
    JournalConstructive Approximation
    Volume49
    DOIs
    Publication statusPublished - 15 Jun 2019

    Keywords

    • Convolution
    • Dunkl transform
    • Generalized translation operator
    • Riesz potential

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