MAXIMAL OPERATORS AND HILBERT TRANSFORMS ALONG FLAT CURVES NEAR L1

DOI10.1017/S1446788709000111zbMath1185.42007MaRDI QIDQ5852035

Neal Bez

Publication date: 26 January 2010

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

maximal operatorHilbert transformweak type estimate

Mathematics Subject Classification ID

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

Cites Work

• Examples of singular maximal functions unbounded on \(L^ p\)
• Operators associated to flat plane curves: \(L^ p\) estimates via dilation methods
• Weak type (1,1) bounds for rough operators
• Maximal functions and Hilbert transforms associated to polynomials
• Maximal operators along piecewise linear curves near $L^1$
• $L^p$-boundedness for the Hilbert transform and maximal operator along a class of nonconvex curves
• The Hilbert Transform for Convex Curves in R n
• A Remark on Singular Calderon-Zygmund Theory
• The Hilbert Transform and Maximal Function Along Flat Curves, Dilations, and Differential Equations
• Singular maximal functions and Radon transforms near L 1
• Singular Integrals and Maximal Functions Associated to Surfaces of Revolution
• Sharp Lorentz space estimates for rough operators

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