Related papers: Sharp inequalities for one-sided Muckenhoupt weigh…

We characterize the weights for the Stieltjes transform and the Calder\'on operator to be bounded on the weighted variable Lebesgue spaces $L_w^{p(\cdot)}(0,\infty)$, assuming that the exponent function $p(\cdot)$ is log-H\"older continuous…

Using a transference result, several inequalities of approximation by entire functions of exponential type in $\mathcal{C}(\mathbf{R})$, the class of bounded uniformly continuous functions defined on $\mathbf{R}:=\left( -\infty ,+\infty…

Matrix weights satisfying a Muckenhoupt $A_p$-condition relative to a family of anisotropic balls in $\mathbb{R}^d$ defined by a pseudo-metric are studied. It is shown that such matrix weights satisfy a doubling condition and a reverse…

In the present work we give a simple method to obtain weighted norm inequalities in Lebesgue spaces $L_{p,\gamma }$ with Muckenhoupt weights $\gamma $. This method is different from celebrated Extrapolation or Interpolation Theory. In this…

In this article, we establish a nearly sharp localized weighted inequality related to Gagliardo and Sobolev seminorms, respectively, with the sharp $A_1$-weight constant or with the specific $A_p$-weight constant when $p\in (1,\infty)$. As…

The main goal of this paper is to provide a complete characterization of the weak-type boundedness of the Hardy-Littlewood maximal operator, $M$, on weighted Lorentz spaces $\Lambda^p_u(w)$, whenever $p>1$. This solves a problem left open…

This is the first part of a series of three articles. In this paper, we obtain weighted norm inequalities for different conical square functions associated with the Heat and the Poisson semigroups generated by a second order divergence form…

We present ten different characterizations of functions satisfying a weak reverse H\"older inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak…

In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function $\Mm$ introduced in \cite{LOPTT} and for multilinear Calder\'on-Zygmund operators. In particular we obtain a sharp mixed…

We dominate non-integral singular operators by adapted sparse operators and derive optimal norm estimates in weighted spaces. Our assumptions on the operators are minimal and our result applies to an array of situations, whose prototype are…

This paper focuses on the operator norm of the truncated Hardy-Littlewood maximal operator $M^b_a$ and the strong truncated Hardy-Littlewood maximal operator $\tilde{M}^{\boldsymbol{b}}_{\boldsymbol{a}}$, respectively. We first present the…

In this note we prove a multilinear version of the reverse H\"older inequality in the theory of Muckenhoupt $A_p$ weights. We give two applications of this inequality to the study of multilinear weighted norm inequalities. First, we prove a…

Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with $\sigma\geq n/2$. The aim of this paper is to study the $A_p$ weights associated to $L$,…

Let T be an arbitrary L^2 bounded Calderon--Zygmund operator, and T_# its maximal truncated version. Then T_# satisfies the following bound for all 1<p<\infty and all weights w\in A_p: \|T_# \|_{L^p(w)} << [w]_{A_p}^{1/p}…

Let $A_1$ and $A_2$ be expansive dilations, respectively, on ${\mathbb R}^n$ and ${\mathbb R}^m$. Let $\vec A\equiv(A_1, A_2)$ and $\mathcal A_p(\vec A)$ be the class of product Muckenhoupt weights on ${\mathbb R}^n\times{\mathbb R}^m$ for…

We present a brief survey of recent results on boundedness of some classical operators within the frameworks of weighted spaces $L^{p(\cdot)}(\varrho)$ with variable exponent $p(x)$, mainly in the Euclidean setting and dwell on a new result…

A description of all the admissible weights similar to the Muckenhoupt class $A_p$ is an open problem for the weighted Morrey spaces. In this paper necessary condition and sufficient condition for two-weight norm inequalities on Morrey…

Let $t\in(0,\infty)$, $p\in(1,\infty)$, $q\in[1,\infty]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical…

Let $A_i$ for $i=1, 2$ be an expansive dilation, respectively, on ${\mathbb R}^n$ and ${\mathbb R}^m$ and $\vec A\equiv(A_1, A_2)$. Denote by ${\mathcal A}_\infty(\rnm; \vec A)$ the class of Muckenhoupt weights associated with $\vec A$. The…

In this paper, we study weighted $L^{p}(w)$ boundedness ($1<p<\infty$ and $w$ a Muckenhoupt $A_{p}$ weight) of singular integrals with homogeneous convolution kernel $K(x)$ on an arbitrary homogeneous group $\mathbb H$ of dimension…