Cristian González-Riquelme
PhD. in mathematics
About me.
I am Cristian González-Riquelme, a postdoctoral researcher at the Instituto Superior Tecnico in Lisbon, working under the supervision of Diogo Oliveira e Silva. Previously, I was a Posdoctoral fellow at ICTP. I obtained my PhD in mathematics at IMPA in 2021, working under the advice of Emanuel Carneiro (you can find my thesis here). I am mainly interested in harmonic analysis. You may find my CV here.
Contact:
cristiangonzalezriquelme95[at]gmail[dot]com
cristian.g.riquelme[at]tecnico[dot]ulisboa[dot]pt
Research.
I have mainly been interested in understanding fine properties of different types of maximal functions. Lately, I've been also interested in sharp inequalities in Fourier analysis. Here are my preprints:
Sharp extension inequalities on finite fields (with D. Oliveira e Silva), 2024, preprint.
Sharp embeddings between weighted Paley-Wiener spaces (with E. Carneiro, L. Oliveira, A. Olivo, S. Ombrosi, A. P. Ramos and M. Sousa), 2023, preprint.
The maximal function of the Devil's staircase is absolutely continuous (with D. Kosz)[Journal], 2022, J. Geom. Anal.
Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level, [Journal], 2021, J. Funct. Anal.
On the continuity of maximal operators of convolution type at the derivative level[Journal], 2021, Israel J. Math.
Continuity of the gradient of the fractional maximal operator on W^{1,1}(R^d) (with D. Beltran, J. Madrid and J. Weigt), [Journal], 2021, Math. Res. Lett.
Sharp inequalities for maximal operators on finite graphs, II (with J. Madrid)[Journal], 2020, J. Math. Anal. Appl.
BV continuity for the uncentered Hardy--Littlewood maximal operator (with D. Kosz)[Journal], 2020, J. Funct. Anal.
Sunrise strategy for the continuity of maximal operators (with E. Carneiro and J. Madrid)[Journal], 2020, J. Anal. Math.
Sharp inequalities for maximal operators on finite graphs (with J. Madrid)[Journal], 2021, J. Geom. Anal.
Sobolev regularity of polar fractional maximal functions [Journal], 2020, Nonlinear Anal.
Gradient bounds for radial maximal functions (with E. Carneiro)[Journal], 2021, Ann. Fenn. Math.