Revista Matemática Iberoamericana


Full-Text PDF (246 KB) | Metadata | Table of Contents | RMI summary
Volume 34, Issue 3, 2018, pp. 1401–1414
DOI: 10.4171/RMI/1029

Published online: 2018-08-27

Sparse domination on non-homogeneous spaces with an application to $A_p$ weights

Alexander Volberg[1] and Pavel Zorin-Kranich[2]

(1) Michigan State University, East Lansing, USA
(2) Universität Bonn, Germany

We extend Lerner's recent approach to sparse domination of Calderón–Zygmund operators to upper doubling (but not necessarily doubling), geometrically doubling metric measure spaces. Our domination theorem, different from the one obtained recently by Conde-Alonso and Parcet, yields a weighted estimate with the sharp power max$(1,1/(p-1))$ of the $A_{p}$ characteristic of the weight.

Keywords: Calderón–Zygmund operators, non-doubling measures, sparse operators

Volberg Alexander, Zorin-Kranich Pavel: Sparse domination on non-homogeneous spaces with an application to $A_p$ weights. Rev. Mat. Iberoamericana 34 (2018), 1401-1414. doi: 10.4171/RMI/1029