Two Weight Bump Conditions for Matrix Weights

  • David Cruz-Uribe OFS
  • Joshua Isralowitz
  • Kabe Moen


In this paper we extend the theory of two weight, \(A_p\) bump conditions to the setting of matrix weights. We prove two matrix weight inequalities for fractional maximal operators, fractional and singular integrals, sparse operators and averaging operators. As applications we prove quantitative, one weight estimates, in terms of the matrix \(A_p\) constant, for singular integrals, and prove a Poincaré inequality related to those that appear in the study of degenerate elliptic PDEs.


Matrix weights \(A_p\) bump conditions Maximal operators Fractional integral operators Singular integral operators Sparse operators Poincaré inequalities p-Laplacian 

Mathematics Subject Classification

Primary 42B20 42B25 42B35 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • David Cruz-Uribe OFS
    • 1
  • Joshua Isralowitz
    • 2
  • Kabe Moen
    • 1
  1. 1.Department of MathematicsUniversity of AlabamaTuscaloosaUSA
  2. 2.Department of Mathematics and StatisticsSUNY AlbanyAlbanyUSA

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