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Now showing items 1-10 of 12

#### Sparse and weighted estimates for generalized Hörmander operators and commutators

(2019)

In this paper a pointwise sparse domination for generalized Ho ̈rmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination ...

#### $A_1$ theory of weights for rough homogeneous singular integrals and commutators

(2019)

Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved:
\[
\|T_\Omega ...

#### Vector-valued operators, optimal weighted estimates and the $C_p$ condition

(2018-09)

In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...

#### Weighted norm inequalities for rough singular integral operators

(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

(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 ...

#### A quantitative approach to weighted Carleson condition

(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 ...

#### Improved A1 − A∞ and related estimates for commutators of rough singular integrals

(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 ...

#### On pointwise and weighted estimates for commutators of Calderón-Zygmund operators

(2017)

In recent years, it has been well understood that a
Calderón-Zygmund operator T is pointwise controlled by a finite
number of dyadic operators of a very simple structure (called the
sparse operators). We obtain a similar ...

#### $A_1$ theory of weights for rough homogeneous singular integrals and commutators

(2016-07-01)

Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved:
\[
\|T_\Omega ...