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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Ioanna Kyrezi and Michel Marias
Journal: Trans. Amer. Math. Soc. 361 (2009), 1053-1067
MSC (2000): Primary 42B15, 42B20, 42B30
Published electronically: September 29, 2008
MathSciNet review: 2452834
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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] $.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04596-0
PII: S 0002-9947(08)04596-0
Keywords: Graph, multiplier, Hardy space, discrete Laplacian
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”.
Dedicated: Dedicated to the memory of Nikos Danikas
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.