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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 | References | Similar Articles | Additional Information

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 $.

References [Enhancements On Off] (What's this?)

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Additional Information

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

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