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#### 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 ...

#### Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators

(Proceedings of the American Mathematical Society, 2017-07)

We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ...

#### 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 ...

#### 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.

#### 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 ...

#### A characterization of two weight norm inequality for Littlewood-Paley $g_{\lambda}^{*}$-function

(Journal of Geometric Analysis, 2017)

Let $n\ge 2$ and $g_{\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+|x-y ...

#### The Calderón problem with corrupted data

(Inverse Problems, 2017-01)

We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, ...

#### Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions

(Transactions of the American Mathematical Society, 2017)

Our main goal in this article is to study mixed norm estimates for
the Cesàro means associated with Dunkl--Hermite expansions on
$\mathbb{R}^d$. These expansions arise when one considers the
Dunkl--Hermite operator ...

#### 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 ...

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

(Advances in Mathematics, 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 ...