Reverse Hölder inequalities for spherical harmonics
Javier Duoandikoetxea · Proceedings of the American Mathematical Society · 1987
We prove that the L p {L^p} -norm with respect to the normalized Lebesgue measure on the sphere of any spherical harmonic of degree k k is bounded by a constant independent of the dimension times its L 2 {L^2} -norm. Several consequences are obtained from this result.