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Systems of singular integral operators on spheres


Author: Daniel A. Levine
Journal: Trans. Amer. Math. Soc. 144 (1969), 493-522
MSC: Primary 43A85
DOI: https://doi.org/10.1090/S0002-9947-1969-0412743-1
MathSciNet review: 0412743
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  • [1] H. Boerner, Representations of groups, North-Holland, Amsterdam, 1963.
  • [2] N. Bourbaki, Éléments de mathématique, Fase. XXVII, Algèbre commutative, Hermann, Paris, 1961.
  • [3] A. P. Calderón, Integrales singulares y sus aplicaciones a ecuaciones diferenciales hiperbolicas, Curos y Seminarios de Matemática, Fasc. 3, Universidad de Buenos Aires, Buenos Aires, 1960. MR 0123834 (23:A1156)
  • [4] -, Singular integrals, Bull. Amer. Math. Soc. 72 (1966), 427-465. MR 0209918 (35:813)
  • [5] A. P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901-921. MR 0100768 (20:7196)
  • [6] R. Godement, ``Localites simples. I and II'' in Séminaire H. Cartan et C. Chevalley, 8$ ^{e}$ année, École Norm. Sup., Paris, 1956.
  • [7] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 0145455 (26:2986)
  • [8] -, Some results on invariant theory, Bull. Amer. Math. Soc. 68 (1962), 367-371. MR 0166303 (29:3580)
  • [9] L. Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501-517. MR 0180740 (31:4970)
  • [10] N. Jacobson, Lie algebras, Interscience, New York, 1966. MR 0143793 (26:1345)
  • [11] J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269-305. MR 0176362 (31:636)
  • [12] B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327-404. MR 0158024 (28:1252)
  • [13] S. Lang, Introduction to algebraic geometry, Interscience, New York, 1958. MR 0100591 (20:7021)
  • [14] D. A. Levine, Singular integral operators on spheres, Ph.D. Thesis, Princeton University, Princeton, N. J., 1968.
  • [15] S. G. Mihlin, Higher-dimensional singular integrals and integral equations, Fizmatgiz, Moscow, 1962; English transl., Pergamon Press, New York, 1965. MR 0155165 (27:5105)
  • [16] B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17-92. MR 0199636 (33:7779)
  • [17] F. D. Murnaghan, The theory of group representations, Johns Hopkins Press, Baltimore, Maryland, 1938.
  • [18] R. S. Palais, ``Differential operators on vector bundles'' in Seminar on the Atiyah-Singer index theorem, Princeton Univ. Press, Princeton, N. J., 1965.
  • [19] R. S. Palais and R. T. Seeley, ``The construction of $ \operatorname{Int}_k$'' in Seminar on the Atiyah-Singer index theorem, Princeton Univ. Press, Princeton, N. J., 1965. MR 0198494 (33:6649)
  • [20] P. Samuel, Méthodes d'algèbre abstraite en géometrie algébrique, Ergebnisse der Mathematik und ihrer Grenzgebeite (N.F.), Heft 4, Springer-Verlag, Berlin, 1955. MR 0072531 (17:300b)
  • [21] R. T. Seeley, Singular integrals on compact manifolds, Amer. J. Math. 81 (1959), 658-690. MR 0110022 (22:905)
  • [22] -, Spherical harmonics, Amer. Math. Monthly 73 (1966), no. 4, Part II, 115-121. MR 0201695 (34:1577)
  • [23] E. M. Stein, Integrales singulières et fonctions differentiables de plusieurs variables, Publications Mathématiques d'Orsay, 1967.
  • [24] E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163-196. MR 0223492 (36:6540)
  • [25] H. Weyl, The classical groups, Princeton Univ. Press, Princeton, N. J., 1946. MR 1488158 (98k:01049)
  • [26] -, Gruppentheorie und Quantenmechanik, 2nd ed., Hirzel, Leipzig, 1931; English transl., Dover, New York, 1950.
  • [27] O. Zariski and P. Samuel, Commutative algebra, Vol. II, Van Nostrand, Princeton, N. J., 1960. MR 0120249 (22:11006)
  • [28] A. Zygmund, Trigonometric series, Cambridge Univ. Press, Cambridge, 1959.

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DOI: https://doi.org/10.1090/S0002-9947-1969-0412743-1
Article copyright: © Copyright 1969 American Mathematical Society

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