| Abstract: |
| We will present recent results about maximal operators of Zygmund-type, i.e. of the form:
$$
Mf(x):=\sup_{B\in B(x)} \frac{1}{|B|} \int_B |f|,
$$
where, for each $x$ (in the $n$-th dimensional Euclidean space), $B(x)$ is a collection of parallelepipeds parallel to the coordinate axes (or, more generally, of convex sets) containing, or being ``close to'' $x$.
Depending on the geometry of sets in the collections $B(x)$, one may wish to understand the optimal weak-type inequality $M$ enjoys.
The talk will detail a few famous cases, and provide some new results on this front.
If time permits, we shall also discuss some issues related to their behavior in BMO or ``moderated'' BMO spaces. |
|