\(L^p\)-Fourier asymptotics, Hardy-type inequality and fractal measures

DOI10.1007/S00605-017-1081-7zbMath1376.42014arXiv1509.04848OpenAlexW2963747513MaRDI QIDQ1675299

K. S. Senthil Raani

Publication date: 27 October 2017

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.04848

zbMATH Keywords

Hausdorff dimensionSalem setsMinkowski contentHardy type inequalityAhlfors-David regular sets

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Hausdorff and packing measures (28A78) Tauberian theorems (40E05)

Cites Work

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• \(L^p\)-integrability, dimensions of supports of Fourier transforms and applications
• Fourier asymptotics of fractal measures
• Hardy's inequality and fractal measures
• Asymptotic properties of solutions of differential equations with simple characteristics
• Mean quadratic variations and Fourier asymptotics of self-similar measures
• \(L^p\)-integrability, supports of Fourier transforms and uniqueness for convolution equations
• Fractal measures and mean \(p\)-variations
• The density theorem and Hausdorff inequality for packing measure in general metric spaces

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