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Proceedings of the American Mathematical Society

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Restriction and extension of Fourier multipliers between weighted $ L^p$ spaces on $ \mathbb{R}^n$ and $ \mathbb{T}^n$


Authors: Kenneth F. Andersen and Parasar Mohanty
Journal: Proc. Amer. Math. Soc. 137 (2009), 1689-1697
MSC (2000): Primary 42B15
Published electronically: December 29, 2008
MathSciNet review: 2470827
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Abstract: Weighted analogues of de Leeuw's restriction theorem for Fourier multipliers on $ L^p(\mathbb{R}^n)$ are obtained. Weighted analogues of related extension theorems for multipliers on $ L^p(\mathbb{T})$ are also considered.


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Additional Information

Kenneth F. Andersen
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
Email: Ken.Andersen@ualberta.ca

Parasar Mohanty
Affiliation: Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, U.P. 208016, India
Email: parasar@iitk.ac.in

DOI: https://doi.org/10.1090/S0002-9939-08-09774-8
Received by editor(s): March 3, 2008
Published electronically: December 29, 2008
Additional Notes: This research was supported in part by the University of Alberta Faculty of Science Research Allowance
Communicated by: Hart F. Smith
Article copyright: © Copyright 2008 American Mathematical Society