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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A result about the Hilbert transform along curves


Author: Linda V. Saal
Journal: Proc. Amer. Math. Soc. 110 (1990), 905-914
MSC: Primary 42B10; Secondary 22E30, 42B25
DOI: https://doi.org/10.1090/S0002-9939-1990-1019281-2
MathSciNet review: 1019281
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Abstract: Let $ G$ be a connected and simply connected, nilpotent Lie group and let $ \gamma :( - 1,1) \to G$ be a (connected) analytic curve such that $ \gamma (0) = 0$. Then the Hilbert transform along $ \gamma $,

$\displaystyle Tf(x) = p.v.\int_{0 < \vert t\vert < 1} {f(x\gamma {{(t)}^{ - 1}})dt/t} ,$

is bounded on $ {L^p}(G),1 < p < \infty $.

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DOI: https://doi.org/10.1090/S0002-9939-1990-1019281-2
Article copyright: © Copyright 1990 American Mathematical Society

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