J. Weigt

collaborators

3 papers

math.CA2025

The centered maximal operator removes the non-concave Cantor part from the gradient

Panu Lahti, Julian Weigt

We study regularity of the centered Hardy--Littlewood maximal function $M f$ of a function $f$ of bounded variation in $R^{d}$ , $d \in N$ . In particular, we show that…

math.CA2025

A Vitali-type lemma for the boundary

Julian Weigt

Take a set of balls in $R^{d}$ . We find a subset of pairwise disjoint balls whose combined perimeter controls the perimeter of the union of the original balls. This can be se…

math.MG2025

Alberti representations, rectifiability of metric spaces and higher integrability of measures satisfying a PDE

David Bate, Julian Weigt

We give a sufficient condition for a Borel subset $E \subset X$ of a complete metric space with $H^{n} (E) < \infty$ to be $n$ -rectifiable. This condition involves a decomposit…