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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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$L^ p$ bounds for spectral multipliers on nilpotent groups
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by Michael Christ PDF
Trans. Amer. Math. Soc. 328 (1991), 73-81 Request permission

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
  • © Copyright 1991 American Mathematical Society
  • 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