170 citations · 272 across the 45 of their papers we have counts for
40 papers · 1 filter
On off-diagonal operators in matrix-weighted spaces
David Cruz-Uribe, Aapo Laukkarinen, Kabe Moen
In this paper we prove matrix-weighted inequalities for fractional operators and their commutators. We do so by developing the theory of convex body domination for such operators.…
The Stein-Weiss inequality in variable exponent Morrey spaces
David Cruz-Uribe, Arash Ghorbanalizadeh, Durvudkhan Suragan
In this paper we prove the Stein-Weiss inequality in variable exponent Morrey spaces over a bounded domain. Our work extends earlier results in the variable exponent Lebesgue and M…
The reverse Hölder inequality for weights with applications to matrix weights
David Cruz-Uribe, Michael Penrod
In this paper we prove a reverse Hölder inequality for the variable exponent Muckenhoupt weights , introduced by the first author, Fiorenza, and Neugeabauer…
Necessary conditions for the boundedness of fractional operators on variable Lebesgue spaces
David Cruz-Uribe, Troy Roberts
In this paper we prove necessary conditions for the boundedness of fractional operators on the variable Lebesgue spaces. More precisely, we find necessary conditions on an exponent…
On the embedding between the variable Lebesgue space and the Orlicz space
David Cruz-Uribe, Amiran Gogatishvili, Tengiz Kopaliani
We give a sharp sufficient condition on the distribution function, , , of the exponent function that implies the embed…
Weighted weak-type inequalities for maximal operators and singular integrals
David Cruz-Uribe, Brandon Sweeting
We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators. We consider a kind…
Convolution Operators in Matrix Weighted, Variable Lebesgue Spaces
David Cruz-Uribe, Michael Penrod
We extend the theory of matrix weights to the variable Lebesgue spaces. The theory of matrix weights has attracted considerable attention beginning with the work of…
Sobolev meets Riesz: a characterization of weighted Sobolev spaces via weighted Riesz bounded variation space
David Cruz-Uribe, Oscar Guzman, Humberro Rafeiro
We introduce weighted Riesz bounded variation spaces defined on an open subset of the -dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the…
Matrix weights, singular integrals, Jones factorization and Rubio de Francia extrapolation
David Cruz-Uribe
In this article we give an overview of the problem of finding sharp constants in matrix weighted norm inequalities for singular integrals, the so-called matrix A2 conjecture. We be…
Hardy-Leray inequalities in variable Lebesgue spaces
David Cruz-Uribe, Durvudkhan Suragan
In this paper, we prove the Hardy-Leray inequality and related inequalities in variable Lebesgue spaces. Our proof is based on a version of the Stein-Weiss inequality in variable L…
Extrapolation and Factorization of matrix weights
Marcin Bownik, David Cruz-Uribe
In this paper we prove the Jones factorization theorem and the Rubio de Francia extrapolation theorem for matrix weights. These results answer longstanding open ques…
The ε-Maximal Operator and Haar Multipliers on Variable Lebesgue Spaces
David Cruz-Uribe, Michael Penrod
C. Stockdale, P. Villarroya, and B. Wick introduced the -maximal operator to prove the Haar multiplier is bounded on the weighted spaces for a class of weights larger t…
A note on the limit of Orlicz norms
David Cruz-Uribe, Scott Rodney
We generalize the well-known inequality that the limit of the norm of a function as is the norm to the scale of Orlicz spaces.
Weighted norm inequalities for the maximal operator on $\Lpp$ over spaces of homogeneous type
David Cruz-Uribe, Jeremy Cummings
Given a space of homogeneous type , we prove strong-type weighted norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces $L…
Neccessary conditions for two weight inequalities for singular integral operators
David Cruz-Uribe, John-Oliver MacLellan
We prove necessary conditions on pairs of measures for a singular integral operator to satisfy weak inequalities, , provided the kernel of s…
On the dual of variable Lebesgue spaces with unbounded exponent
Alex Amenta, Jose M. Conde-Alonso, David Cruz-Uribe +1
We study the dual space of the variable Lebesgue space $\Lp$ with unbounded exponent function $\pp$ and provide an answer to a question posed in~[fiorenza-cruzuribe2013]. Our appro…
Weak endpoint bounds for matrix weights
David Cruz-Uribe, Joshua Isralowitz, Kabe Moen +2
We prove quantitative matrix weighted endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calderón-Zygmund operators, and commutators of CZOs with scalar…
Multilinear fractional Calderón-Zygmund operators on weighted Hardy spaces
David Cruz-Uribe, Kabe Moen, Hanh Nguyen
We prove norm estimates for multilinear fractional integrals acting on weighted and variable Hardy spaces. In the weighted case we develop ideas we used for multilinear singular in…
A new approach to norm inequalities on weighted and variable Hardy spaces
David Cruz-Uribe, Kabe Moen, Hanh Nguyen
We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlockin…
The Calderón operator and the Stieltjes transform on variable Lebesgue spaces with weights
David Cruz-Uribe, Estefania Dalmasso, Francisco Martin-Reyes +1
We characterize the weights for the Stieltjes transform and the Calderón operator to be bounded on the weighted variable Lebesgue spaces , assuming that t…
Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces
David Cruz-Uribe, Oscar Mauricio Guzman
We extend the theory of weighted norm inequalities on variable Lebesgue spaces to the case of bilinear operators. We introduce a bilinear version of the variable $\A_\pp$ condition…
Modular inequalities for the maximal operator in variable Lebesgue spaces
David Cruz-Uribe, Giovanni Di Fratta, Alberto Fiorenza
A now classical result in the theory of variable Lebesgue spaces due to Lerner [A. K. Lerner, On modular inequalities in variable spaces, Archiv der Math. 85 (2005), no. 6, 5…
The boundedness of multilinear Calderón-Zygmund operators on weighted and variable Hardy spaces
David Cruz-Uribe, Kabe Moen, Hanh Van Nguyen
We establish the boundedness of the multilinear Calderón-Zygmund operators from a product of weighted Hardy spaces into a weighted Hardy or Lebesgue space. Our results generalize t…
Embeddings between grand, small and variable Lebesgue spaces
David Cruz-Uribe, Alberto Fiorenza, Oscar Guzman
We give conditions on the exponent function that imply the existence of embeddings between grand, small and variable Lebesgue spaces. We construct examples to show that…