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Lp Bounds for Spectral Multipliers on Nilpotent Groups

Michael Christ
Transactions of the American Mathematical Society
Vol. 328, No. 1 (Nov., 1991), pp. 73-81
DOI: 10.2307/2001877
Stable URL: http://www.jstor.org/stable/2001877
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Lp Bounds for Spectral Multipliers on Nilpotent Groups
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Abstract

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.

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