Logarithmic \(L^p\) bounds for maximal directional singular integrals in the plane

DOI10.1007/s12220-012-9340-2zbMath1302.42022arXiv1203.6624OpenAlexW2023104208MaRDI QIDQ472008

Francesco Di Plinio, Ciprian Demeter

Publication date: 18 November 2014

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.6624

zbMATH Keywords

Kakeya maximal functionCalderón-Zygmund convolution kernelmaximal directional singular integrals

Mathematics Subject Classification ID

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

Related Items (14)

A sharp estimate for the Hilbert transform along finite order lacunary sets of directions ⋮ An analogy of the Carleson-Hunt theorem with respect to Vilenkin systems ⋮ \(L^2\) bounds for a maximal directional Hilbert transform ⋮ Maximal functions along convex curves with lacunary directions ⋮ Square functions for bi-Lipschitz maps and directional operators ⋮ A maximal function for families of Hilbert transforms Along homogeneous curves ⋮ Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^p$ boundedness ⋮ Directional square functions ⋮ Singular integrals along lacunary directions in \(\mathbb{R}^n\) ⋮ Maximal functions associated with families of homogeneous curves: L^p bounds for P ≤ 2 ⋮ Almost-orthogonality principles for certain directional maximal functions ⋮ On logarithmic bounds of maximal sparse operators ⋮ A multiplier inclusion theorem on product domains ⋮ A guide to Carleson's theorem

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