Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$H^{1}$-bounds for spectral multipliers on graphs

Authors: Ioanna Kyrezi and Michel Marias
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1311-1320
MSC (2000): Primary 42B15, 42B20, 42B30
Published electronically: December 12, 2003
MathSciNet review: 2053335
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that certain spectral multipliers associated with the discrete Laplacian on graphs satisfying the doubling volume property and the Poincaré inequality are bounded on the Hardy space $H^{1}$.

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

  • 1. G. Alexopoulos, Spectral multipliers on discrete groups, Bull. London Math. Soc., 33, (2001), 417-424. MR 2002d:22010
  • 2. G. Alexopoulos, $L^{p}$ bounds for spectral multipliers from Gaussian estimates of the transition kernels, preprint.
  • 3. M. Christ, $L^{p}$ bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc., 328, (1991), 73-81. MR 92k:42017
  • 4. R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc., 83, (1977), 569-645. MR 56:6264
  • 5. T. Coulhon, Random walks and geometry on infinite graphs, Lectures notes on analysis on metric spaces, Trento, C.I.R.M., 1999, Luigi Ambrosio, Francesco Serra Cassano, ed., Scuola Normale Superiore di Pisa, (2000), 5-23.
  • 6. T. Delmotte, Parabolic Harnack inequality and estimates of Markov chains on graphs, Rev. Mat. Iberoamericana, 15, (1999), 181-232.MR 2000b:35103
  • 7. M. Marias and E. Russ, $H^{1}$-boundedness of Riesz transforms and imaginary powers of the Laplacian on Riemmanian manifolds, Ark. Mat., 41, (2003), 115-132.
  • 8. E. Russ, $H^{1}-L^{1}$ boundedness of Riesz transforms on Riemannian manifolds and on graphs, Potential Anal., 14, (2001), 301-330.MR 2003b:42029
  • 9. E. Russ, Temporal regularity for random walks and Riesz transforms on graphs for $1\leq p\leq2$, preprint.
  • 10. L. Saloff-Coste, Parabolic Harnack inequality for divergence form second order differential operators, Potential Anal., 4, (1995), 429-467.MR 96m:35031
  • 11. A. Sikora and J. Wright, Imaginary powers of Laplace operators, Proc. Amer. Math. Soc., 129, (2001), 1745-1754. MR 2001m:35076
  • 12. E. M. Stein, Topics in Harmonic Analysis related to the Littlewood-Paley Theory, Annals of Mathematical Studies, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 40:6176

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B15, 42B20, 42B30

Retrieve articles in all journals with MSC (2000): 42B15, 42B20, 42B30

Additional Information

Ioanna Kyrezi
Affiliation: Department of Applied Mathematics, University of Crete, Iraklio 714.09, Crete, Greece

Michel Marias
Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54.124, Greece

Keywords: Graphs, spectral multipliers, imaginary powers of the Laplacian, Hardy spaces, Markov kernels
Received by editor(s): February 24, 2002
Published electronically: December 12, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society