Maximal operators and Fourier transforms of self-similar measures

DOI10.1016/j.chaos.2005.02.038zbMath1081.28009OpenAlexW2035147991MaRDI QIDQ813522

Huo-Jun Ruan, Yong Lin

Publication date: 13 February 2006

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2005.02.038

zbMATH Keywords

Fourier transform\(L^p\)-boundednessmaximal operatornonlinear self-similar measure

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Fractals (28A80)

Cites Work

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• Averages in the plane over convex curves and maximal operators
• Averages over hypersurfaces. Smoothness of generalized Radon transforms
• Maximal functions and Fourier transforms
• Mean quadratic variations and Fourier asymptotics of self-similar measures
• Asymptotic behavior of multiperiodic functions \(G(x)=\prod_{n=1}^\infty g(x/2^n)\)
• Maximal averages over surfaces
• Fractal measures and mean \(p\)-variations
• Self-Similar Measures and Their Fourier Transforms. II
• Nonlinear self-similar measures and their Fourier transforms

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