Cristian Gonz'alez-Riquelme

activity

20192022

collaborators

10 papers

math.CA2022

The maximal function of the Devil's staircase is absolutely continuous

Cristian González-Riquelme, Dariusz Kosz

We study the problem of whether the centered Hardy--Littlewood maximal function of a singular function is absolutely continuous. For a parameter $d \in (0, 1)$ and a closed set $E\s…

math.CA2021

Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level

Cristian González-Riquelme

We prove the continuity of the map $f \mapsto (M f)^{'}$ from $W^{1, 1} (R)$ to $L^{1} (R)$ , where $M$ is the centered Hardy-Littlewood maximal operator. This solves a que…

math.CA2021

On the continuity of maximal operators of convolution type at the derivative level

Cristian González-Riquelme

In this paper we study a question related to the continuity of maximal operators of convolution type acting on $W^{1, 1} (R)$ . We prove that the map $u \mapsto (u^{*})^{'}$ is c…

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

Sharp inequalities for maximal operators on finite graphs, II

Cristian González-Riquelme, José Madrid

Let $M_{G}$ be the centered Hardy-Littlewood maximal operator on a finite graph $G$ . We find $p \to \infty lim ∥ M_{G} ∥_{p}^{p}$ when $G$ is the start graph ( $S_{n}$ ) an…

math.CA2020

BV continuity for the uncentered Hardy--Littlewood maximal operator

Cristian González-Riquelme, Dariusz Kosz

We prove the continuity of the map $f \mapsto M f$ from $B V (R)$ to itself, where $M$ is the uncentered Hardy--Littlewood maximal operator. This answ…

The maximal function of the Devil's staircase is absolutely continuous

Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level

On the continuity of maximal operators of convolution type at the derivative level

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

Sharp inequalities for maximal operators on finite graphs, II

BV continuity for the uncentered Hardy--Littlewood maximal operator

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