Julian Weigt

activity

20182026

most citedWeak differentiability for fractional maximal functions of general

L^{p}

functions on domains

8 citations · 9 across the 7 of their papers we have counts for

collaborators

11 papers

math.CA2026

On the variation and asymptotics of maximal functions

Emanuel Carneiro, Julian Weigt

In this paper we present partial progress towards two conjectures on the variation of maximal operators of convolution type $M_{φ}$ , associated to non-negative and radial de…

math.CA2026

Sharp higher order regularity of discrete maximal functions

Sung-Yi Liao, José Madrid, Eyvindur Palsson +1

We derive sharp $ℓ^{p} (Z)$ bounds for the $k$ th derivative of the discrete uncentered maximal operator applied to characteristic functions $f : Z \to {0, 1}$ in the…

math.CA2023★ 1 cited

Weighted fractional Poincaré inequalities via isoperimetric inequalities

Kim Myyryläinen, Carlos Pérez, Julian Weigt

Our main result is a weighted fractional Poincaré-Sobolev inequality improving the celebrated estimate by Bourgain-Brezis-Mironescu. This also yields an improvement of the classica…

math.CA2021

The Variation of the Uncentered Maximal Operator with respect to Cubes

Julian Weigt

We consider the maximal operator with respect to uncentered cubes on Euclidean space with arbitrary dimension. We prove that for any function with bounded variation, the variation…

math.CA2021

The one-dimensional centred maximal function diminishes the variation of indicator functions

Constantin Bilz, Julian Weigt

We prove sharp local and global variation bounds for the centred Hardy--Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both…

math.CA2021

Continuity of the gradient of the fractional maximal operator on $W^{1, 1} (R^{d})$

David Beltran, Cristian González-Riquelme, José Madrid +1

We establish that the map $f \mapsto ∣\nabla M_{α} f ∣$ is continuous from $W^{1, 1} (R^{d})$ to $L^{q} (R^{d})$ , where $α \in (0, d)$ , $q = \frac{d}{d - α}$ and $\mathca…

math.CA2020

Endpoint Sobolev Bounds for Fractional Hardy-Littlewood Maximal Operators

Julian Weigt

Let $0 < α < d$ and $1 \leq p < d / α$ . We present a proof that for all $f \in W^{1, p} (R^{d})$ both the centered and the uncentered Hardy-Littlewood fractional maximal operator $\math…

math.CA2020

Variation of the dyadic maximal function

Julian Weigt

We prove that for the dyadic maximal operator $M$ and every locally integrable function $f \in L_{loc}^{1} (R^{d})$ with bounded variation, also $M f$ is…

math.CA2020

Variation of the uncentered maximal characteristic Function

Julian Weigt

Let $M$ be the uncentered Hardy-Littlewood maximal operator or the dyadic maximal operator and $d \geq 1$ . We prove that for a set $E \subset R^{d}$ of finite perimeter…

math.CA2019★ 8 cited

Weak differentiability for fractional maximal functions of general $L^{p}$ functions on domains

João P. G. Ramos, Olli Saari, Julian Weigt

Let $Ω \subset R^{n}$ be bounded a domain. We prove under certain structural assumptions that the fractional maximal operator relative to $Ω$ maps $L^{p} (Ω) \to W^{1, p} (Ω)$ …

math.FA2018

Almost-Orthogonality of Restricted Haar-Functions

Julian Weigt

We consider the Haar functions $h_{I}$ on dyadic intervals. We show that if $p > \frac{2}{3}$ and $E \subset [0, 1]$ then the set of all functions $∥ h_{I} 1_{E} ∥_{2}^{- 1} h_{I} 1_{E}$ with $|I\cap E|\ge…

On the variation and asymptotics of maximal functions

Sharp higher order regularity of discrete maximal functions

Weighted fractional Poincaré inequalities via isoperimetric inequalities

The Variation of the Uncentered Maximal Operator with respect to Cubes

The one-dimensional centred maximal function diminishes the variation of indicator functions

Continuity of the gradient of the fractional maximal operator on W1,1(Rd)

Endpoint Sobolev Bounds for Fractional Hardy-Littlewood Maximal Operators

Variation of the dyadic maximal function

Variation of the uncentered maximal characteristic Function

Weak differentiability for fractional maximal functions of general Lp functions on domains

Almost-Orthogonality of Restricted Haar-Functions

Continuity of the gradient of the fractional maximal operator on $W^{1, 1} (R^{d})$

Weak differentiability for fractional maximal functions of general $L^{p}$ functions on domains