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Reverse Hölder inequalities for spherical harmonics

Author: Javier Duoandikoetxea
Journal: Proc. Amer. Math. Soc. 101 (1987), 487-491
MSC: Primary 42B99; Secondary 26D10, 31B05
MathSciNet review: 908654
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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.

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Article copyright: © Copyright 1987 American Mathematical Society

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