Singular maximal functions and Radon transforms near L^1

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We show that some singular maximal functions and singular Radon transforms satisfy a weak type $L\log\log L$ inequality. Examples include the maximal function and Hilbert transform associated to averages along a parabola. The weak type inequality yields pointwise convergence results for functions which are locally in $L\log\log L$.
32 pages

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Classical Analysis and ODEs

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http://salesiana.dossiersoluciones.com/handle/123456789/64069

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205156
 http://arxiv.org/abs/math/0205156

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arXiv