\(L^p\)-estimates for singular integrals and maximal operators associated with flat curves on the Heisenberg group

DOI10.1215/S0012-7094-02-11434-3zbMath1012.42013MaRDI QIDQ1857110

Joonil Kim

Publication date: 15 June 2003

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

maximal operatorHeisenberg groupLittlewood-Paley decompositionsingular Radon transformbounded doubling timemultiparameter Marcinkiewicz multiplier theorem

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Analysis on real and complex Lie groups (22E30) Integral operators (47G10) Analysis on other specific Lie groups (43A80)

Related Items (3)

Singular Radon transforms and maximal functions under convexity assumptions ⋮ Marcinkiewicz multiplier theorem for the Weyl functional calculus ⋮ Singular Radon transforms along odd curves on the Heisenberg group

Cites Work

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• Hilbert transforms for convex curves
• Operators associated to flat plane curves: \(L^ p\) estimates via dilation methods
• Hilbert transforms along curves. I: Nilpotent groups
• Estimates for Wainger's singular integrals along curves
• Harmonic analysis on nilpotent groups and singular integrals. II: Singular kernels supported on submanifolds
• Maximal functions for convex curves
• Maximal functions and Hilbert transforms along variable flat curves
• Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups. I
• \(L^ 2\)-estimates for a class of singular oscillatory integrals
• Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups. II
• Singular and maximal Radon transforms: Analysis and geometry
• The Weyl functional calculus
• Noncommutative microlocal analysis. I
• 𝐿^{𝑝} estimates for maximal functions and Hilbert transforms along flat convex curves in 𝐑²
• Harmonic Analysis in Phase Space. (AM-122)
• Differentiation in lacunary directions
• Problems in harmonic analysis related to curvature
• Hilbert Transforms Along Curves in the Heisenberg Group
• Hilbert Transforms and Maximal Functions Associated to Flat Curves on the Heisenberg Group
• Sur les multiplicateurs des séries de Fourier

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