### Recent Submissions

• #### On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians ﻿

(Communications on pure and applied analysis, 2019-09)
We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ...
• #### Bloom type upper bounds in the product BMO setting ﻿

(Journal of Geometric Analysis, 2019-04-08)
• #### Weighted norm inequalities for rough singular integral operators ﻿

(Journal of Geometric Analysis, 2018-08-17)
In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...
• #### On Bloom type estimates for iterated commutators of fractional integrals ﻿

(Indiana University Mathematics Journal, 2018-04)
In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ...
• #### Quantitative weighted estimates for singular integrals and commutators ﻿

(2018-02-27)
In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe ...
• #### Bilinear representation theorem ﻿

(Transactions of the American Mathematical Society, 2018-01-01)
We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ...
• #### Improved A1 − A∞ and related estimates for commutators of rough singular integrals ﻿

(Proceedings of the Edinburgh Mathematical Society, 2017)
An $A_1-A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n-1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ...
• #### Weighted mixed weak-type inequalities for multilinear operators ﻿

(Studia Mathematica, 2017)
In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ...