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Singular integrals on nilpotent Lie groups


Author: Robert S. Strichartz
Journal: Proc. Amer. Math. Soc. 53 (1975), 367-374
MSC: Primary 43A22; Secondary 22E30
DOI: https://doi.org/10.1090/S0002-9939-1975-0420140-6
MathSciNet review: 0420140
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Abstract: Convolution operators $ Tf(x) = \smallint f(x{y^{ - 1}})K(y)\;dy$ on a class of nilpotent Lie groups are shown to be bounded on $ {L^p},\;1 < p < \infty $, provided the Euclidean Fourier transform of $ K$ (with respect to a coordinate system in which the group multiplication is in a special form) satisfies familiar ``multiplier'' conditions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0420140-6
Keywords: Singular integrals, nilpotent Lie group, $ {L^p}$ boundedness, multiplier transformations
Article copyright: © Copyright 1975 American Mathematical Society

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