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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Author(s): Ioanna Kyrezi; Michel Marias
Journal: Trans. Amer. Math. Soc. 361 (2009), 1053-1067.
MSC (2000): Primary 42B15, 42B20, 42B30
Posted: 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: 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
Posted: 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
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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