Reverse hölder’s inequality for spherical harmonics

Feng Dai, Han Feng, Sergey Tikhonov

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    3 Citations (Scopus)

    Abstract

    © 2015 American Mathematical Society. This paper determines the sharp asymptotic order of the following reverse Holder inequality for spherical harmonics Yn of degree n on the unit sphere Sd-1 of Rd as n→∞: ║Yn║Lq(sd-1)≤Cnα(p,q)║Yn║Lp(Sd-1), 0 <p<q ≤∞. In many cases, these sharp estimates turn out to be significantly better than the corresponding estimates in the Nikolskii inequality for spherical polynomials. Furthermore, they allow us to improve two recent results on the restriction conjecture and the sharp Pitt inequalities for the Fourier transform on Rd.
    Original languageEnglish
    Pages (from-to)1041-1051
    JournalProceedings of the American Mathematical Society
    Volume144
    Issue number3
    DOIs
    Publication statusPublished - 1 Mar 2016

    Keywords

    • Polynomial inequalities
    • Restriction theorems
    • Spherical harmonics

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