Characterization of rearrangement invariant spaces with fixed points for the Hardy-Littlewood maximal operator

Joaquim Martın

Universitat Autònoma de Barcelona

We characterize the rearrangement invariant spaces for which there exists a non-constant fixed point, for the Hardy-Littlewood maximal operator. The main result that we prove is that the space $L^{\frac{n}{n-2},\infty}(\mathbb{R}^{n})\cap L^{\infty }(\mathbb{R}^{n})$ is minimal among those having this property.