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#### End-point estimates, extrapolation for multilinear muckenhoupt classes, and applications

(2019)

In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. ...

#### Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates

(2018-09)

We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that
$$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...

#### 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 ...

#### Weighted mixed weak-type inequalities for multilinear operators

(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 ...

#### Quantitative weighted mixed weak-type inequalities for classical operators

(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 ...

#### Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer

(2016-01-01)

In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2].