$H^{p}$-bounds for spectral multipliers on graphs
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- by Ioanna Kyrezi and Michel Marias PDF
- Trans. Amer. Math. Soc. 361 (2009), 1053-1067 Request permission
Abstract:
We study the boundedness on the Hardy spaces $H^{p}$ of spectral multiplier operators associated with the discrete Laplacian on a weighted graph. We assume that the graph satisfies the doubling volume property and a Poincaré inequality. We prove that there is $p_{0}\in \left ( 0,1\right )$, depending on the geometry of the graph, such that if the multiplier satisfies a condition similar to the one we have in the classical Hörmander multiplier theorem, then the corresponding operator is bounded on $H^{p}$, $p\in \left ( p_{0},1\right ]$.References
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Additional Information
- Ioanna Kyrezi
- Affiliation: Department of Applied Mathematics, University of Crete, Iraklion 714.09, Crete, Greece
- Email: kyrezi@tem.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): November 14, 2005
- Received by editor(s) in revised form: May 15, 2007
- Published electronically: September 29, 2008
- Additional Notes: The first author was partially supported by a NATO (Greece) fellowship and the second author by the EPEAK program Pythagoras II (Greece) and the European TMR Network “Harmonic Analysis”.
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 1053-1067
- MSC (2000): Primary 42B15, 42B20, 42B30
- DOI: https://doi.org/10.1090/S0002-9947-08-04596-0
- MathSciNet review: 2452834
Dedicated: Dedicated to the memory of Nikos Danikas