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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.

42B20Singular and oscillatory integrals, several variables
Full Text: DOI
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