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• W2891657554 abstract "In this paper, we establish the two weight commutator of Calder'on--Zygmund operators in the sense of Coifman--Weiss on spaces of homogeneous type, by studying the weighted Hardy and BMO space for $A_2$ weight and by proving the sparse operator domination of commutators. The main tool here is the Haar basis and the adjacent dyadic systems on spaces of homogeneous type, and the construction of a suitable version of a sparse operator on spaces of homogeneous type. As applications, we provide a two weight commutator theorem (including the high order commutator) for the following Calder'on--Zygmund operators: Cauchy integral operator on $mathbb R$, Cauchy--Szego projection operator on Heisenberg groups, Szego projection operators on a family of unbounded weakly pseudoconvex domains, Riesz transform associated with the sub-Laplacian on stratified Lie groups, as well as the Bessel Riesz transforms (one-dimension and high dimension)." @default.
• W2891657554 created "2018-09-27" @default.
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• W2891657554 date "2018-09-21" @default.
• W2891657554 modified "2023-09-23" @default.
• W2891657554 title "Two weight commutators on spaces of homogeneous type and applications" @default.
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• W2891657554 doi "https://doi.org/10.48550/arxiv.1809.07942" @default.
• W2891657554 hasPublicationYear "2018" @default.
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