Reverse hölder’s inequality for spherical harmonics

Feng Dai; Han Feng; Sergey Tikhonov

doi:10.1090/proc/12986

Reverse hölder’s inequality for spherical harmonics

Feng Dai, Han Feng, Sergey Tikhonov

Research output: Contribution to journal › Article › Research › peer-review

7 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 language	English
Pages (from-to)	1041-1051
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	3
DOIs	https://doi.org/10.1090/proc/12986
Publication status	Published - 1 Mar 2016

Keywords

Polynomial inequalities
Restriction theorems
Spherical harmonics

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10.1090/proc/12986

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title = "Reverse h{\"o}lder{\textquoteright}s inequality for spherical harmonics",

abstract = "{\textcopyright} 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.",

keywords = "Polynomial inequalities, Restriction theorems, Spherical harmonics",

author = "Feng Dai and Han Feng and Sergey Tikhonov",

year = "2016",

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doi = "10.1090/proc/12986",

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journal = "Proceedings of the American Mathematical Society",

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T1 - Reverse hölder’s inequality for spherical harmonics

AU - Dai, Feng

AU - Feng, Han

AU - Tikhonov, Sergey

PY - 2016/3/1

Y1 - 2016/3/1

N2 - © 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.

AB - © 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.

KW - Polynomial inequalities

KW - Restriction theorems

KW - Spherical harmonics

U2 - 10.1090/proc/12986

DO - 10.1090/proc/12986

M3 - Article

SN - 0002-9939

VL - 144

SP - 1041

EP - 1051

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

Reverse hölder’s inequality for spherical harmonics

Abstract

Keywords

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