Related papers: Two weight inequality for vector-valued positive d…

We consider the weak to strong type problem for two weight norm inequalities for Calder\'on-Zygmund operators with doubling weights. We show that if a Calder\'on-Zygmund operator T is weak type (2,2) with doubling weights, then it is strong…

Let $E$ and $G$ be two Banach function spaces, let $T \in \mathcal{L}(E,Y)$, and let ${\langle X,Y \rangle}$ be a Banach dual pair. In this paper we give conditions for which there exists a (necessarily unique) bounded linear operator…

We study the two-weighted estimate \[ \bigg\|\sum_{k=0}^na_k(x)\int_0^xt^kf(t)dt|L_{q,v}(0,\infty)\bigg\|\leq c\|f|L_{p,u}(0,\infty)\|,\tag{$*$} \] where the functions $a_k(x)$ are not assumed to be positive. It is shown that for $1<p\leq…

In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator $T$ with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for…

In this paper a two weight criterion for multidimensional geometric mean operator in variable exponent Lebesgue space is proved. Also, we found a criterion on weight functions expressing one-dimensional Hardy inequality via a certain…

In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted…

We study new weighted estimates for the 2-fold product of Hardy-Littlewood maximal operators defined by $M^{\otimes}(f,g):= MfMg$. This operator appears very naturally in the theory of bilinear operators such as the bilinear…

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 characterize the Banach lattices with the Hardy-Littlewood property by using maximal operators defined by semigroups of operators associated with the inverse Gauss measure.

We establish necessary and sufficient conditions on a weight pair $(v,w)$ governing the boundedness of the Riesz potential operator $I_{\alpha}$ defined on a homogeneous group $G$ from $L^p_{dec,r}(w, G)$ to $L^q(v, G)$, where…

We characterize strong type and weak type inequalities with two weights for positive operators on filtered measure spaces. These estimates are probabilistic analogues of two-weight inequalities for positive operators associated to the…

In this paper, we show that the $q$-variation for differential operator is not bounded in $L^p(\mathbb{R};L^{\infty}(\mathbb{R}))$ for any $1<p<\infty$. As a consequence, the $q$-variation operator can not be used to characterize the…

An algebra of bounded linear operators on a Banach space is said to be {\em strongly compact} if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be {\em strongly…

This paper develops the function and operator theory of Hardy--Carleson--type analytic tent spaces $AT_q^\infty(\omega)$ induced by radial weights $\omega$ satisfying a two-sided doubling condition. We first characterize the positive Borel…

We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the…

We study trace inequalities of the type $$ \| T_k f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d\sigma)}, \qquad f \in L^p(d\sigma), $$ in the ``upper triangle case'' $1 \leq q<p$ for integral operators $T_k$ with positive kernels, where $d\sigma$ and…

The boundedness of the small Hankel operator $h_f^\nu(g)=P_\nu(f\bar{g})$, induced by an analytic symbol $f$ and the Bergman projection $P_\nu$ associated to $\nu$, acting from the weighted Bergman space $A^p_\om$ to $A^q_\nu$ is…

In recent years, it has been well understood that a Calder\'on-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 pointwise…

We consider a two weight $L^{p}(\mu) \to L^{q}(\nu)$-inequality for well localized operators as defined and studied by F. Nazarov, S. Treil and A. Volberg when $p=q=2$. A counterexample of F. Nazarov shows that the direct analogue of these…

We give a characterization of the two-weight inequality for a simple vector-valued operator. Special cases of our result have been considered before in the form of the weighted Carleson embedding theorem, the dyadic positive operators of…