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

Abstract

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 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.

12 pages. v3: corrections following referee's report

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• Dyadic harmonic analysis and weighted inequalities: the sparse revolution
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• Sparse bounds for maximal rough singular integrals via the Fourier transform
• Weighted Estimates for Rough Bilinear Singular Integrals via Sparse Domination
• Sharp dimension free bound for the Bakry-Riesz vector
• Sparse bounds for pseudo-multipliers associated to Grushin operators, I
• Sparse domination and weighted estimates for rough bilinear singular integrals