English

Singular maximal functions and Radon transforms near L^1

Classical Analysis and ODEs 2007-05-23 v1

Abstract

We show that some singular maximal functions and singular Radon transforms satisfy a weak type LloglogLL\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 LloglogLL\log\log L.

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Cite

@article{arxiv.math/0205156,
  title  = {Singular maximal functions and Radon transforms near L^1},
  author = {Andreas Seeger and Terence Tao and James Wright},
  journal= {arXiv preprint arXiv:math/0205156},
  year   = {2007}
}

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32 pages