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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the $L^2 \to L^{\infty}$ norms of spectral multipliers
of ``quasi-homogeneous'' operators
on homogeneous groups


Author: Adam Sikora
Journal: Trans. Amer. Math. Soc. 351 (1999), 3743-3755
MSC (1991): Primary 42B15; Secondary 43A22, 35P99
DOI: https://doi.org/10.1090/S0002-9947-99-02501-5
Published electronically: April 27, 1999
MathSciNet review: 1670160
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the $L^2 \to L^{\infty}$ norms of spectral projectors and spectral multipliers of left-invariant elliptic and subelliptic second-order differential operators on homogeneous Lie groups. We obtain a precise description of the $L^2 \to L^{\infty}$ norms of spectral multipliers for some class of operators which we call quasi-homogeneous. As an application we prove a stronger version of Alexopoulos' spectral multiplier theorem for this class of operators.


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Additional Information

Adam Sikora
Affiliation: Centre for Mathematics and Its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia
Email: sikora@maths.anu.edu.au, sikora@math.uni.wroc.pl

DOI: https://doi.org/10.1090/S0002-9947-99-02501-5
Received by editor(s): November 10, 1996
Published electronically: April 27, 1999
Article copyright: © Copyright 1999 American Mathematical Society