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 language | English |
|---|---|
| Pages (from-to) | 607-647 |
| Number of pages | 41 |
| Journal | American Journal of Mathematics |
| Volume | 126 |
| Issue number | 3 |
| Publication status | Published - Jun 2004 |