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Lp Bounds for Spectral Multipliers on Nilpotent Groups
Transactions of the American Mathematical Society
Vol. 328, No. 1 (Nov., 1991), pp. 73-81
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2001877
Page Count: 9
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A criterion is given for the Lp 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.
Transactions of the American Mathematical Society © 1991 American Mathematical Society