Sharp \(L^{2}\) bound of maximal Hilbert transforms over arbitrary sets of directions

DOI10.1016/j.jmaa.2007.01.022zbMath1284.42036OpenAlexW2040863204MaRDI QIDQ2642096

Joonil Kim

Publication date: 20 August 2007

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.01.022

zbMATH Keywords

Fourier transform

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Linear operators on function spaces (general) (47B38)

Related Items (4)

\(L^2\) bounds for a maximal directional Hilbert transform ⋮ Logarithmic \(L^p\) bounds for maximal directional singular integrals in the plane ⋮ $L^p$ estimates for maximal averages along one-variable vector fields in ${\mathbf R} ^2$ ⋮ Almost-orthogonality principles for certain directional maximal functions

Cites Work

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• A remark on maximal operators along directions in \(\mathbb R^2\)
• Maximal operators over arbitrary sets of directions
• On differentiation of integrals

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