A result about the Hilbert transform along curves
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- by Linda V. Saal PDF
- Proc. Amer. Math. Soc. 110 (1990), 905-914 Request permission
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 $\gamma$, \[ Tf(x) = p.v.\int _{0 < |t| < 1} {f(x\gamma {{(t)}^{ - 1}})dt/t} ,\] is bounded on ${L^p}(G),1 < p < \infty$.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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