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Singular maximal functions and Radon transforms near L1
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 126, Number 3, June 2004
- pp. 607-647
- 10.1353/ajm.2004.0020
- Article
- Additional Information
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.