Abstract
We prove that the restriction to an affine subspace of such a Fourier multiplier is still a Fourier multiplier, generalizing a celebrated theorem of de Leeuw for Fourier multipliers of L p. This may be seen as a complement to the spectacular result that such Fourier multipliers are continuous, which has been recently proved by Kazaniecki and Wojciechowski.
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Bonami, A. (2016). Fourier Multipliers of the Homogeneous Sobolev Space Ẇ 1,1 . In: Pereyra, M., Marcantognini, S., Stokolos, A., Urbina, W. (eds) Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1). Association for Women in Mathematics Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-30961-3_7
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DOI: https://doi.org/10.1007/978-3-319-30961-3_7
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