Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Multipliers for spherical harmonic expansions


Author: Robert S. Strichartz
Journal: Trans. Amer. Math. Soc. 167 (1972), 115-124
MSC: Primary 43A75
DOI: https://doi.org/10.1090/S0002-9947-1972-0306823-9
MathSciNet review: 0306823
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] R. Askey and S. Wainger, On the behavior of special classes of ultraspherical expansions. II, J. Analyse 15 (1965), 221-244. MR 33 #1510. MR 0193290 (33:1510)
  • [2] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190. MR 29 #5097. MR 0167830 (29:5097)
  • [3] W. Littman, Multipliers in $ {L^p}$ and interpolation, Bull. Amer. Math. Soc. 71 (1965), 764-766. MR 31 #3792. MR 0179544 (31:3792)
  • [4] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92. MR 33 #7779. MR 0199636 (33:7779)
  • [5] J. Peetre, Applications de la théorie des espaces d'interpolation dans l'analyse harmonique, Ricerche Mat. 15 (1966), 3-36. MR 36 #4266. MR 0221214 (36:4266)
  • [6] E. M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory, Ann. of Math. Studies, no. 63, Princeton Univ. Press, Princeton, N. J.; Univ. of Tokyo Press, Tokyo, 1970. MR 40 #6176. MR 0252961 (40:6176)
  • [7] -, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1970. MR 0290095 (44:7280)
  • [8] -, $ {L^p}$ boundedness of certain convolution operators, Bull. Amer. Math. Soc. 77 (1971), 404-405. MR 0276757 (43:2497)
  • [9] R. Strichartz, A functional calculus for elliptic pseudodifferential operators (to appear).
  • [10] M. H. Taibleson, a) On the theory of Lipschitz spaces of distributions on Euclidean n-space. I. Principal properties, J. Math. Mech. 13 (1964), 407-479. MR 29 #462. b) II. Translation invariant, J. Math. Mech. 14 (1965), 821-839. MR 31 #5087. MR 0163159 (29:462)
  • [11] N. Ja. Vilenkin, Special functions and the theory of group representations, ``Nauka", Moscow, 1965; English transl., Transl. Math. Monographs, vol. 22, Amer. Math. Soc., Providence, R. I., 1968. MR 35 #420. MR 0229863 (37:5429)
  • [12] N. Weiss, Multipliers on compact Lie groups, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 930-931. MR 0283499 (44:730)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A75

Retrieve articles in all journals with MSC: 43A75


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0306823-9
Keywords: Spherical harmonics, $ {L^p}$ multipliers, Littlewood-Paley theory
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society