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15 September 2002 Lp-estimates for singular integrals and maximal operators associated with flat curves on the Heisenberg group
Joonil Kim
Duke Math. J. 114(3): 555-593 (15 September 2002). DOI: 10.1215/S0012-7094-02-11434-3

Abstract

The maximal function along a curve $(t,\gamma(t),t\gamma(t))$ on the Heisenberg group is discussed. The $L\sp p$-boundedness of this operator is shown under the doubling condition of $\gamma\sp \prime$ for convex $\gamma$ in $\mathbb {R}\sp +$. This condition also applies to the singular integrals when $\gamma$ is extended as an even or odd function. The proof is based on angular Littlewood-Paley decompositions in the Heisenberg group.

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Joonil Kim. "Lp-estimates for singular integrals and maximal operators associated with flat curves on the Heisenberg group." Duke Math. J. 114 (3) 555 - 593, 15 September 2002. https://doi.org/10.1215/S0012-7094-02-11434-3

Information

Published: 15 September 2002
First available in Project Euclid: 18 June 2004

MathSciNet: MR1924572
Digital Object Identifier: 10.1215/S0012-7094-02-11434-3

Subjects:
Primary: 42B20
Secondary: 47G10

Rights: Copyright © 2002 Duke University Press

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Vol.114 • No. 3 • 15 September 2002
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