Related papers: Sharp weighted bounds for fractional integral oper…
In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_\gamma$ on these new function spaces. Furthermore, the…
We establish sharp two-sided weighted bounds on the fundamental solution to the fractional Schr\"{o}dinger operator using the method of desingularizing weights.
In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain weighted weak and…
This is the first part of a series of four articles. In this work, we are interested in weighted norm estimates. We put the emphasis on two results of different nature: one is based on a good-$\lambda$ inequality with two-parameters and the…
In this paper we prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted $L^p$…
Let $(X,d,\mu)$ be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions. In this paper, the boundedness of multilinear fractional integral operator in this setting is…
We give weighted norm inequalities for the maximal fractional operator $ \mathcal M_{q,\beta}$ of Hardy-Littlewood and the fractional integral $I_{\gamma}$. These inequalities are established between $(L^{q},L^{p}) ^{\alpha}(X,d,\mu)$…
In this paper we investigate the boundedness of sublinear operators generated by fractional integrals as well as sublinear operators generated by Calder\`on-Zygmund operators on generalized weighted Morrey spaces and generalized weighted…
In this paper we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann-Liouville fractional integral and derivative operators on a compact of the real axis.This approach has some advantages and allows us to…
We prove Rubio de Francia extrapolation results in Lebesgue and grand Lebesgue spaces for quasi monotone functions with $QB_{\beta,p}$ weights. The extrapolation in Lebesgue spaces with the weight class $QB_{\beta,\infty}$ has also been…
We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the…
With rectangular doubling weight, a~generalized Hardy-Littlewood-Sobolev inequality for rectangular fractional integral operators is verified. The result is a~nice application of $M$-linear embedding theorem for dyadic rectangles.
This paper is devoted to studying the boundedness of multilinear operartors and their commutators on generalized weighted Morrey spaces, which includes multilinear fractional maximal operator and multilinear fractional integral operator.…
In this paper we address the problem of estimating the operator norm of the embeddings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By…
We derive criteria governing two-weight estimates for multilinear fractional integrals and appropriate maximal functions. The two and one weight problems for multi(sub)linear strong fractional maximal operators are also studied; in…
A necessary condition and a sufficient condition for one weight norm inequalities on Morrey spaces to hold are given for the fractional maximal operator and the fractional integral operator. We clarify the difference between the behavior of…
The present paper is devoted to the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. In particular, Sobolev, trace and weighted inequalities with power weights for potential operators are…
Two-weight norm estimates for the double Hardy transforms and strong fractional maximal functions are established in variable exponent Lebesgue spaces. Derived conditions are simultaneously necessary and sufficient in the case when the…
The purpose of this note is to prove that the strong Christ-Goldberg maximal function is bounded. This is a matrix weighted maximal operator appearing in the theory of matrix weighted norm inequalities. Related to this we record the Rubio…
In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operator from just one space to the full range of weighted spaces,…