Duke Mathematical Journal

On the boundedness of functions of (pseudo-) differential operators on compact manifolds

A. Seeger and C. D. Sogge

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 59, Number 3 (1989), 709-736.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077308165

Digital Object Identifier
doi:10.1215/S0012-7094-89-05932-2

Mathematical Reviews number (MathSciNet)
MR1046745

Zentralblatt MATH identifier
0698.35169

Subjects
Primary: 58G15
Secondary: 35S05: Pseudodifferential operators 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx]

Citation

Seeger, A.; Sogge, C. D. On the boundedness of functions of (pseudo-) differential operators on compact manifolds. Duke Math. J. 59 (1989), no. 3, 709--736. doi:10.1215/S0012-7094-89-05932-2. https://projecteuclid.org/euclid.dmj/1077308165


Export citation

References

  • [1] A. Carbery, Variants of the Calderón-Zygmund theory for $L\sp p$-spaces, Rev. Mat. Iberoamericana 2 (1986), no. 4, 381–396.
  • [2] A. Carbery, G. Gasper, and W. Trebels, Radial Fourier multipliers of $L\spp(\bf R\sp2)$, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), no. 10, Phys. Sci., 3254–3255.
  • [3] A. Carbery and A. Seeger, Conditionally convergent series of linear operators on $L\sp p$-spaces and $L\sp p$-estimates for pseudodifferential operators, Proc. London Math. Soc. (3) 57 (1988), no. 3, 481–510.
  • [4] M. Christ, On almost everywhere convergence of Bochner-Riesz means in higher dimensions, Proc. Amer. Math. Soc. 95 (1985), no. 1, 16–20.
  • [5] F. M. Christ and C. D. Sogge, The weak type $L\sp 1$ convergence of eigenfunction expansions for pseudodifferential operators, Invent. Math. 94 (1988), no. 2, 421–453.
  • [6] R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque, vol. 57, Soc. Math. France, Paris, 1978.
  • [7] C. Fefferman, A note on spherical summation multipliers, Israel J. Math. 15 (1973), 44–52.
  • [8] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107–115.
  • [9] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193.
  • [10] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, preprint.
  • [11] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), no. 1, 27–42.
  • [12] L. Hörmander, The spectral function of an elliptic operator, Acta Math. 88 (1968), 341–370.
  • [13] L. Hörmander, Estimates for translation invariant operators in $L^p$ spaces, Acta Math. 104 (1960), 93–139.
  • [14] L. Hörmander, Fourier integral operators I, Acta Math. 127 (1971), no. 1-2, 79–183.
  • [15] C. Kenig, R. Stanton, and P. Tomas, Divergence of eigenfunction expansions, J. Funct. Anal. 46 (1982), no. 1, 28–44.
  • [16] L. Päivarinta, Pseudo differential operators in Hardy-Triebel spaces, Z. Anal. Anwendungen 2 (1983), no. 3, 235–242.
  • [17] J. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123–130.
  • [18] J. Peetre, Classes de Hardy sur les variétés, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), no. 7, Aii, A439–A441.
  • [19] A. Seeger, On quasiradial Fourier multipliers and their maximal functions, J. Reine Angew. Math. 370 (1986), 61–73.
  • [20] A. Seeger, Necessary conditions for quasiradial Fourier multipliers, Tohoku Math. J. (2) 39 (1987), no. 2, 249–257.
  • [21] A. Seeger, Some inequalities for singular convolution operators in $L^ p$-spaces, Trans. Amer. Math. Soc. 308 (1988), no. 1, 259–272.
  • [22] C. D. Sogge, Concerning the $L^p$ norm of spectral clusters for second order elliptic operators on compact manifolds, J. Funct. Anal. 77 (1988), no. 1, 123–138.
  • [23] C. D. Sogge, On the convergence of Riesz means on compact manifolds, Ann. of Math. (2) 126 (1987), no. 2, 439–447.
  • [24] C. D. Sogge, Lecture notes for course at Univ. Chicago, 1988.
  • [25] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30, Princeton Univ. Press, Princeton, N.J., 1970.
  • [26] R. Strichartz, The Hardy space $H\sp1$ on manifolds and submanifolds, Canad. J. Math. 24 (1972), 915–925.
  • [27] R. Strichartz, A functional calculus for elliptic pseudo-differential operators, Amer. J. Math. 94 (1972), 711–722.
  • [28] M. Taylor, Pseudo-differential Operators, Princeton Mathematical Series, vol. 34, Princeton Univ. Press, Princeton N.J., 1981.
  • [29] H. Triebel, Theory of function spaces, Monographs in Mathematics, vol. 78, Birkhäuser Verlag, Basel, Boston, Stuttgart, 1983.
  • [30] H. Triebel, Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds, Ark. Mat. 24 (1986), no. 2, 299–337.