$L^p$ estimates for maximal averages along one-variable vector fields in ${\mathbf R} ^2$

DOI10.1090/S0002-9939-08-09583-XzbMath1173.42008arXiv0802.0183OpenAlexW1982086395MaRDI QIDQ3617583

Michael Bateman

Publication date: 30 March 2009

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

Full work available at URL: https://arxiv.org/abs/0802.0183

zbMATH Keywords

maximal functioncovering argument

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25)

Related Items (4)

Single annulus estimates for the variation-norm Hilbert transforms along Lipschitz vector fields ⋮ Single annulus \(L^p\) estimates for Hilbert transforms along vector fields ⋮ Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^p$ boundedness ⋮ Maximal averages along a planar vector field depending on one variable

Cites Work

• A geometric proof of the strong maximal theorem
• Maximal functions associated to rectangles with uniformly distributed directions
• Classes of singular integral operators along variable lines
• Sharp \(L^{2}\) bound of maximal Hilbert transforms over arbitrary sets of directions
• On a conjecture of E. M. Stein on the Hilbert transform on vector fields
• On differentiation of integrals
• On unboundedness of maximal operators for directional Hilbert transforms

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