The maximal Hilbert transform along nonconvex curves

DOI10.1186/1029-242X-2012-191zbMath1280.42008WikidataQ59289815 ScholiaQ59289815MaRDI QIDQ386678

Hong Hai Liu

Publication date: 10 December 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

maximal functionLittlewood-Paley theorymaximal Hilbert transformnonconvex curve

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

Cites Work

• Hilbert transforms for convex curves
• Operators associated to flat plane curves: \(L^ p\) estimates via dilation methods
• \(L^ p\) bounds for Hilbert transforms along convex curves
• 𝐿^{𝑝} estimates for maximal functions and Hilbert transforms along flat convex curves in 𝐑²
• Differentiation in lacunary directions
• Problems in harmonic analysis related to curvature
• The Hilbert Transform and Maximal Function Along Flat Curves, Dilations, and Differential Equations

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