Related papers: The rectangular fractional integral operators
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…
We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of fractional Poincar\'e inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results…
This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…
We prove a sharp Hardy inequality for fractional integrals for functions that are supported on a general domain. The constant is the same as the one for the half-space and hence our result settles a recent conjecture of Bogdan and Dyda.
We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…
We investigate one and two weight norm inequalities for product fractional integrals. We show that in the one weight case, most of the 1 parameter theory carries over to the 2 parameter setting. However, in the two weight case, apart from…
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.…
We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.
By means of a counter-example we show that the multilinear fractional operator is not bounded from a product of Hardy spaces into a Hardy space.
This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional…
Given a space of homogeneous type we give sufficient conditions on a variable exponent {p(.)} so that the fractional maximal operator {M_{\eta}} maps {L^{p(.)}(X)} to {L^{q(.)}(X)}, where {1/p(.) - 1/q(.) = {\eta}}. In the endpoint case we…
This is the second in our series of papers concerning some reversed Hardy--Littlewood--Sobolev inequalities. In the present work, we establish the following sharp reversed Hardy--Littlewood--Sobolev inequality on the half space $\mathbb…
We give a constructive proof of the factorization theorem for the classical Hardy space in terms of fractional integral operator. Moreover, the result is extended to the multilinear case and weighted case. As an application, we obtain the…
Three novel multilinear embedding estimates for the fractional Laplacian are obtained in terms of trace integrals restricted to the diagonal. The resulting sharp inequalities may be viewed as extensions of the Hardy-Littlewood-Sobolev…
We establishe an affine Hardy-Littlewood-Sobolev inequality concerning two different functions which is stronger than the classical Hardy-Littlewood-Sobolev inequality. Furthermore, we also prove reverse inequalities for the new…
Two-weight criteria of various type for the Hardy-Littlewood maximal operator and singular integrals in variable exponent Lebesgue spaces defined on the real line are established.
In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for…
We prove a weighted Sobolev inequality and a Hardy inequality on manifolds with nonnegative Ricci curvature satisfying an inverse doubling volume condition. It enables us to obtain rigidity results for Ricci flat manifolds, generalizing…
The rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands…
We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…