Multipliers for spherical harmonic expansions

Strichartz, Robert S.

doi:10.1090/S0002-9947-1972-0306823-9

Multipliers for spherical harmonic expansions
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by Robert S. Strichartz PDF

Trans. Amer. Math. Soc. 167 (1972), 115-124 Request permission

Abstract:

Sufficient conditions are given for an operator on the sphere that commutes with rotations to be bounded in ${L^p}$. The conditions are analogous to those of Hörmander’s well-known theorem on Fourier multipliers.

References

Richard Askey and Stephen Wainger, On the behavior of special classes of ultraspherical expansions. I, II, J. Analyse Math. 15 (1965), 193–220. MR 193290, DOI 10.1007/BF02787693
A.-P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190. MR 167830, DOI 10.4064/sm-24-2-113-190
Walter Littman, Multipliers in $L^{p}$ and interpolation, Bull. Amer. Math. Soc. 71 (1965), 764–766. MR 179544, DOI 10.1090/S0002-9904-1965-11382-9
B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17–92. MR 199636, DOI 10.1090/S0002-9947-1965-0199636-9
Jaak Peetre, Applications de la théorie des espaces d’interpolation dans l’analyse harmonique, Ricerche Mat. 15 (1966), 3–36 (French). MR 221214
Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory. , Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961
Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
E. M. Stein, $L^{p}$ boundedness of certain convolution operators, Bull. Amer. Math. Soc. 77 (1971), 404–405. MR 276757, DOI 10.1090/S0002-9904-1971-12716-7

A functional calculus for elliptic pseudodifferential operators

Mitchell H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean $n$-space. I. Principal properties, J. Math. Mech. 13 (1964), 407–479. MR 0163159
N. Ja. Vilenkin, Special functions and the theory of group representations, Translations of Mathematical Monographs, Vol. 22, American Mathematical Society, Providence, R.I., 1968. Translated from the Russian by V. N. Singh. MR 0229863, DOI 10.1090/mmono/022
Norman J. Weiss, Multipliers on compact Lie groups, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 930–931. MR 283499, DOI 10.1073/pnas.68.5.930