J. Weigt

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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.CA2024

Sobolev bounds and counterexamples for the second derivative of the maximal function in one dimension

Julian Weigt

We investigate the question whether the $L^{1} (R)$ -norm of the second derivative of the uncentered Hardy-Littlewood maximal function can be bounded by a constant times the $L…