Julian Weigt

activity

20182021

collaborators

5 papers

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

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.CA2019

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…

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)

Variation of the dyadic maximal 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