𝐿^{𝑝} bounds for spectral multipliers on nilpotent groups

Christ, Michael

doi:10.1090/S0002-9947-1991-1104196-7

$L^ p$ bounds for spectral multipliers on nilpotent groups
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by Michael Christ

Trans. Amer. Math. Soc. 328 (1991), 73-81

DOI: https://doi.org/10.1090/S0002-9947-1991-1104196-7

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Abstract:

A criterion is given for the ${L^p}$ boundedness of a class of spectral multiplier operators associated to left-invariant, homogeneous subelliptic second-order differential operators on nilpotent Lie groups, generalizing a theorem of Hörmander for radial Fourier multipliers on Euclidean space. The order of differentiability required is half the homogeneous dimension of the group, improving previous results in the same direction.

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