REVERSE HÖLDER’S INEQUALITY FOR SPHERICAL HARMONICS

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)1041-1051
Journal / PublicationProceedings of the American Mathematical Society
Volume144
Issue number3
Online published20 Nov 2015
Publication statusPublished - Mar 2016
Externally publishedYes

Abstract

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 → ∞: 

            ║YnLq (Sd-1) Cnα(p,q)YnLp (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.

Research Area(s)

  • Polynomial inequalities, Restriction theorems, Spherical harmonics

Citation Format(s)

REVERSE HÖLDER’S INEQUALITY FOR SPHERICAL HARMONICS. / DAI, Feng; FENG, Han; TIKHONOV, Sergey.
In: Proceedings of the American Mathematical Society, Vol. 144, No. 3, 03.2016, p. 1041-1051.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review