Singular maximal functions and radon transforms near L

A Seeger, T Tao, J Wright

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)607-647
Number of pages41
JournalAmerican Journal of Mathematics
Volume126
Issue number3
Publication statusPublished - Jun 2004

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