$H^{1}$-bounds for spectral multipliers on graphs
HTML articles powered by AMS MathViewer
- by Ioanna Kyrezi and Michel Marias PDF
- Proc. Amer. Math. Soc. 132 (2004), 1311-1320 Request permission
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
- Georgios K. Alexopoulos, Spectral multipliers on discrete groups, Bull. London Math. Soc. 33 (2001), no. 4, 417–424. MR 1832553, DOI 10.1017/S0024609301008165
- G. Alexopoulos, $L^{p}$ bounds for spectral multipliers from Gaussian estimates of the transition kernels, preprint.
- Michael Christ, $L^p$ bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc. 328 (1991), no. 1, 73–81. MR 1104196, DOI 10.1090/S0002-9947-1991-1104196-7
- Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5
- 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.
- Thierry Delmotte, Parabolic Harnack inequality and estimates of Markov chains on graphs, Rev. Mat. Iberoamericana 15 (1999), no. 1, 181–232. MR 1681641, DOI 10.4171/RMI/254
- 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.
- Emmanuel Russ, $H^1$-$L^1$ boundedness of Riesz transforms on Riemannian manifolds and on graphs, Potential Anal. 14 (2001), no. 3, 301–330. MR 1822920, DOI 10.1023/A:1011269629655
- E. Russ, Temporal regularity for random walks and Riesz transforms on graphs for $1\leq p\leq 2$, preprint.
- L. Saloff-Coste, Parabolic Harnack inequality for divergence-form second-order differential operators, Potential Anal. 4 (1995), no. 4, 429–467. Potential theory and degenerate partial differential operators (Parma). MR 1354894, DOI 10.1007/BF01053457
- Adam Sikora and James Wright, Imaginary powers of Laplace operators, Proc. Amer. Math. Soc. 129 (2001), no. 6, 1745–1754. MR 1814106, DOI 10.1090/S0002-9939-00-05754-3
- 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
Additional Information
- Ioanna Kyrezi
- Affiliation: Department of Applied Mathematics, University of Crete, Iraklio 714.09, Crete, Greece
- Email: kyrezi@fourier.math.uoc.gr
- Michel Marias
- Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54.124, Greece
- Email: marias@math.auth.gr
- Received by editor(s): February 24, 2002
- Published electronically: December 12, 2003
- Communicated by: Andreas Seeger
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1311-1320
- MSC (2000): Primary 42B15, 42B20, 42B30
- DOI: https://doi.org/10.1090/S0002-9939-03-07356-8
- MathSciNet review: 2053335