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Boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces: equivalent characterizations. (English) Zbl 1230.42020

The authors discuss the boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces. They prove that the boundedness of Calderón-Zygmund operators on \(L^2\) is equivalent to either the boundedness of \(T\) from the atomic Hardy space \(H^1\) to \(L^{1,\infty}\) or from \(H^1\) to \(L^1\) on the measure space \((X,d,\mu)\) in the sense of T. Hytönen. The main tool is the Calderón-Zygmund decomposition established by B.T. Anh and X. T. Duong.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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