Reverse Hölder inequalities for spherical harmonics
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- by Javier Duoandikoetxea PDF
- Proc. Amer. Math. Soc. 101 (1987), 487-491 Request permission
Abstract:
We prove that the ${L^p}$-norm with respect to the normalized Lebesgue measure on the sphere of any spherical harmonic of degree $k$ is bounded by a constant independent of the dimension times its ${L^2}$-norm. Several consequences are obtained from this result.References
- William Beckner, Inequalities in Fourier analysis, Ann. of Math. (2) 102 (1975), no. 1, 159–182. MR 385456, DOI 10.2307/1970980
- Javier Duoandikoetxea and José L. Rubio de Francia, Estimations indépendantes de la dimension pour les transformées de Riesz, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 7, 193–196 (French, with English summary). MR 780616
- Christopher D. Sogge, Oscillatory integrals and spherical harmonics, Duke Math. J. 53 (1986), no. 1, 43–65. MR 835795, DOI 10.1215/S0012-7094-86-05303-2
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 487-491
- MSC: Primary 42B99; Secondary 26D10, 31B05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0908654-1
- MathSciNet review: 908654