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$ L\sp p$ bounds for spectral multipliers on nilpotent groups


Author: Michael Christ
Journal: Trans. Amer. Math. Soc. 328 (1991), 73-81
MSC: Primary 42B15; Secondary 22E30, 35P99, 43A22
DOI: https://doi.org/10.1090/S0002-9947-1991-1104196-7
MathSciNet review: 1104196
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1104196-7
Keywords: Spectral multiplier, nilpotent Lie group, subellipticity, heat kernel
Article copyright: © Copyright 1991 American Mathematical Society

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