Related papers: Two Weight Inequalities for Positive Operators: Do…

Let $\mu$ be a non-negative Borel measure on $R^d$ satisfying that the measure of a cube in $R^d$ is smaller than the length of its side raised to the $n$-th power, $0<n\leq d$. In this article we study the class of weights related to the…

We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we…

Let $1<p\leq \infty$ and let $n\geq 2.$ It was proved independently by C. Calder\'on, R. Coifman and G. Weiss that the dyadic maximal function \begin{equation*}…

Let $\delta\in(0,1]$ and $T$ be a $\delta$-Calder\'on-Zygmund operator. Let $w$ be in the Muckenhoupt class $A_{1+\delta/n}({\mathbb R}^n)$ satisfying $\int_{{\mathbb R}^n}\frac {w(x)}{1+|x|^n}\,dx<\infty$. When $b\in{\rm BMO}(\mathbb…

We prove an extrapolation result for general operators under some weak assumptions on the boundedness of the operator. In particular, we show that if the operator is weakly bounded on some L^{p_{0}}(w), for all "flat" weights, w in…

We study mapping properties of the centered Hardy--Littlewood maximal operator $\mathcal{M}$ acting on Lorentz spaces $L^{p,q}(\mathfrak{X})$ in the context of certain non-doubling metric measure spaces $\mathfrak{X}$. The special class of…

Bounded and compact differences of two composition operators acting from the weighted Bergman space $A^p_\omega$ to the Lebesgue space $L^q_\nu$, where $0<q<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights…

In this paper, we show a weighted Hardy inequality in a limiting case for functions in weighted Sobolev spaces with respect to an invariant measure. We also prove that the constant in the left-hand side of the inequality is optimal. As…

Let $M=(0,\infty)_r\times Y$ be a $d$-dimensional ($d\ge 3$) metric cone with metric<br/>$g=dr^2+r^2h$, where $(Y,h)$ is a closed Riemannian manifold. Let<br/>$H=\Delta+V_0/r^2$ be the associated Schrodinger operator, with<br/>$V_0\in…

Let $p:\R\to(1,\infty)$ be a globally log-H\"older continuous variable exponent and $w:\R\to[0,\infty]$ be a weight. We prove that the Cauchy singular integral operator $S$ is bounded on the weighted variable Lebesgue space…

We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.

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…

We study weighted norm inequalities of $(p,r)$-type, $ \Vert \mathbf{G} (f \, d \sigma) \Vert_{L^r(\Omega, d\sigma)} \le C \Vert f \Vert_{L^p(\Omega, \sigma)}, \quad \forall \, f \in L^p(\sigma),$ for $0 < r < p$ and $p>1$, where…

We find necessary and sufficient conditions on weights $u_1, u_2, v_1, v_2$, i.e. measurable, positive, and finite, a.e. on $(a,b)$, for which there exists a positive constant $C$ such that for given $0 < p_1,q_1,p_2,q_2 <\infty$ the…

In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calder\'on commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the…

In this paper we obtain a new boundedness criterion for the maximal operator $M$ on variable exponent spaces $L^{p(\cdot)}$. It is formulated in terms of the variable exponent analogue of the well known weighted $A_{\infty}$ condition.

Let $\omega$ and $\nu$ be radial weights on the unit disc of the complex plane such that $\omega$ admits the doubling property $\sup_{0\le r<1}\frac{\int_r^1 \omega(s)\,ds}{\int_{\frac{1+r}{2}}^1 \omega(s)\,ds}<\infty$. Consider the one…

We obtain $L^p(w)$ bounds for the Carleson operator ${\mathcal C}$ in terms of the $A_q$ constants $[w]_{A_q}$ for $1\le q\le p$. In particular, we show that, exactly as for the Hilbert transform, $\|{\mathcal C}\|_{L^p(w)}$ is bounded…

For a given second-order linear elliptic operator $L$ which admits a positive minimal Green function, and a given positive weight function $W$, we introduce a family of weighted Lebesgue spaces $L^p(\phi_p)$ with their dual spaces, where…

We provide quantitative weighted estimates for the $L^p(w)$ norm of a maximal operator associated to cube skeletons in $\mathbb{R}^n$. The method of proof differs from the usual in the area of weighted inequalities since there are no…