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Singular maximal functions and Radon transforms near L^1

Andreas Seeger·Terence Tao·James Wright
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Abstract

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 $L\log\log L$.

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Andreas Seeger, Terence Tao, James Wright. 2002-05-14. Singular maximal functions and Radon transforms near L^1. https://arxiv.org/abs/math/0205156

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