Singular maximal functions and Radon transforms near L^1

Details Singular maximal functions and Radon transforms near L^1 Singular maximal functions and Radon transforms near L^1

2002-05-14

arxiv.org/abs/math/0205156v1

Mathematics

Classical Analysis and ODEs

32 pages

Scientific paper

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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