Now showing items 32-49 of 49

• #### A quantitative approach to weighted Carleson condition ﻿

(Concrete Operators, 2017-05-05)
Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator $\mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0$ are ...
• #### Quantitative weighted estimates for rough homogeneous singular integrals ﻿

(Israel Journal of Mathematics, 2017-03-11)
We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...
• #### Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function ﻿

(Journal of Geometric Analysis, 2019-12)
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. ...
• #### 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 ...
• #### Quantitative weighted mixed weak-type inequalities for classical operators ﻿

(Indiana University Mathematics Journal, 2016-06-30)
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ...
• #### Reconstruction of the Derivative of the Conductivity at the Boundary ﻿

(2019-08)
We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness ...
• #### Reverse Hölder Property for Strong Weights and General Measures ﻿

(Journal of Geometric Analysis, 2016-06-30)
We present dimension-free reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ...
• #### Sharp weighted estimates involving one supremum ﻿

(Comptes Rendus Mathematique, 2017-07)
In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ...
• #### Sparse bounds for maximal rough singular integrals via the Fourier transform ﻿

(Annales de l'institut Fourier, 2019-03-12)
We prove a quantified sparse bound for the maximal truncations of convolution-type singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by Conde-Alonso, Culiuc, ...
• #### Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition ﻿

(Michigan Mathematical Journal, 2017-04-01)
In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-Hörmander condition, then $T$ can be dominated by multilinear sparse operators.
• #### Three Observations on Commutators of Singular Integral Operators with BMO Functions ﻿

(AWM-Springer Series, Harmonic Analysis, Partial Differentail Equations, Complex Analysis, Banach Spaces, and Operator Theory, 2016-07-01)
• #### 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 ...
• #### 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 ...