Extending sets by means of the maximal function; continuity estimates
Let $B$ be a collection of bounded open sets in $\mathbb R^n$ such as balls, cubes, or ndimensional rectangles with sides parallel to the coordinate axes. We let $M_B f(x)$ denote the maximal operator associated with the collection $B$. We show that the enlargement of a set $E$ defined by the $(1-\varepsilon)$ superlevel set of the maximal function $M_B$ converges to the set $E$ as $\varepsilon$ goes to zero, in a suitable geometric sense, defined in accordance with the geometry of $B$. For more general collections $B$ (such as homothecy invariant collections of convex sets) we state a corresponding conjecture. This talk reports on joint work with Paul A. Hagelstein (Baylor). http://cvgmt.sns.it/seminar/383/
When
Tue Mar 11, 2014 3pm – 4pm Coordinated Universal Time
Where
Dipartimento di Matematica Università di Roma "Tor Vergata" (map)
