2 citations · 5 across the 7 of their papers we have counts for
8 papers
Pointwise Riesz potential bounds for rough singular integrals
Kabe Moen, Carlos Pérez
We give a complete characterization of the kernels $Ω\in \Lup^1(\Sp)$ for which the rough singular integral $\T_Ω$ and the associated maximal operator $\M_Ω$ satisfy pointwise boun…
From generalized Poincaré to Poincaré-Sobolev inequalities via self-improving methods
Alejandro Claros, Carlos Pérez, Linfei Zheng
We establish several improvements to the main results of [PR19] and [CP21], refining the seminal self-improving method for generalized Poincaré inequalities from [FPW98, MP98]. The…
Bourgain-Brezis-Mironescu formula for Riesz Potentials
Alejandro Claros, Carlos Pérez
We identify the Bourgain-Brezis-Mironescu pointwise limit of the nonlocal potential operator , , where denotes the Riesz potential and $\ma…
A new look at subrepresentation formulas
Cong Hoang, Kabe Moen, Carlos Pérez
We extend the subrepresentation formula in several ways. First, we consider more general -potential operators on the right-hand side an…
A homage to Guido Weiss and his leadership of the Saint Louis team: Commutators of Singular Integrals and Sobolev inequalities
Cong Hoang, Kabe Moen, Carlos Pérez
We extend some classical Sobolev-type inequalities for linear and non-linear commutators.
Pointwise estimates for rough operators with applications to Sobolev inequalities
Cong Hoang, Kabe Moen, Carlos Pérez
We investigate Sobolev inequalities for several rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this…
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…
On the weighted inequality between the Gagliardo and Sobolev seminorms
Ritva Hurri-Syrjänen, Javier C. Martínez-Perales, Carlos Pérez +1
We prove weighted inequalities between the Gagliardo and Sobolev seminorms and also between the Marcinkiewicz quasi-norm and the Sobolev seminorm. With weights we improve ear…