Key points are not available for this paper at this time.
The purpose of this work is to show that the fractional maximal operator has somewhat unexpected regularity properties. The main result shows that the fractional maximal operator maps Lp-spaces boundedly into certain first-order Sobolev spaces. It is also proved that the fractional maximal operator preserves first-order Sobolev spaces. This extends known results for the Hardy-Littlewood maximal operator. 2000 Mathematics Subject Classification 42B25, 46E35.
Kinnunen et al. (Mon,) studied this question.