Restriction and extension of Fourier multipliers between weighted 𝐿^{𝑝} spaces on ℝⁿ and 𝕋ⁿ

Andersen, Kenneth; Mohanty, Parasar

doi:10.1090/S0002-9939-08-09774-8

Restriction and extension of Fourier multipliers between weighted $L^p$ spaces on $\mathbb {R}^n$ and $\mathbb {T}^n$
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by Kenneth F. Andersen and Parasar Mohanty

Proc. Amer. Math. Soc. 137 (2009), 1689-1697

DOI: https://doi.org/10.1090/S0002-9939-08-09774-8

Published electronically: December 29, 2008

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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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