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Two Weight Bump Conditions for Matrix Weights

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama, Box 870350 , Tuscaloosa, AL, 35487, USA

    David Cruz-Uribe OFS & Kabe Moen

  2. Department of Mathematics and Statistics, SUNY Albany, 1400 Washington Ave., Albany, NY, 12222, USA

    Joshua Isralowitz

Authors
  1. David Cruz-Uribe OFS
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  2. Joshua Isralowitz
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  3. Kabe Moen
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Correspondence to Kabe Moen.

Additional information

The first author is supported by NSF Grant DMS-1362425 and research funds from the Dean of the College of Arts and Sciences, the University of Alabama. The second and third authors are supported by the Simons Foundation.

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Cruz-Uribe OFS, D., Isralowitz, J. & Moen, K. Two Weight Bump Conditions for Matrix Weights. Integr. Equ. Oper. Theory 90, 36 (2018). https://doi.org/10.1007/s00020-018-2455-5

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  • DOI: https://doi.org/10.1007/s00020-018-2455-5

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