Two weight inequalities for positive operators: doubling cubes

  • Wei Chen

    Yangzhou University, China and Georgia Institute of Technology, Atlanta, USA
  • Michael T. Lacey

    Georgia Institute of Technology, Atlanta, USA
Two weight inequalities for positive operators: doubling cubes cover

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Abstract

For the maximal operator on , and , there is a finite constant so that this holds. For all weights on , the operator is bounded from if and only if the pair of weights satisfy the two weight condition, and this testing inequality holds:

for all cubes for which there is a cube satisfying , and . This was recently proved by Kangwei Li and Eric Sawyer. We give a short proof, which is easily seen to hold for several closely related operators.

Cite this article

Wei Chen, Michael T. Lacey, Two weight inequalities for positive operators: doubling cubes. Rev. Mat. Iberoam. 36 (2020), no. 7, pp. 2209–2216

DOI 10.4171/RMI/1197