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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, or from H 1 to L 1 on the measure space (X,d,μ) in the sense of T. Hytönen. The main tool is the Calderón-Zygmund decomposition established by B.T. Anh and X. T. Duong.
MSC:
42B20Singular and oscillatory integrals, several variables
References:
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