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

2018; Royal Spanish Mathematical Society; Volume: 34; Issue: 3 Linguagem: Inglês

10.4171/rmi/1029

2235-0616

Alexander Volberg, Pavel Zorin‐Kranich,

Advanced Mathematical Physics Problems

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