Boundedness of Calderón–Zygmund operators on non-homogeneous metric measure spaces: Equivalent characterizations
Copyright policy )Boundedness of Calderón–Zygmund operators on non-homogeneous metric measure spaces: Equivalent characterizations
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.
- Xiamen University China (People's Republic of)
- Beijing Normal University China (People's Republic of)
Dominating function, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Geometrically doubling, atom, Applied Mathematics, H-1, Metric measure space, upper doubling, Hardy space, Atom, geometrically doubling, Upper doubling, metric measure space, 515, dominating function, THEOREM, Calderón-Zygmund operator, Calderón–Zygmund operator, NON-DOUBLING MEASURES, Analysis, BMO
Dominating function, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Geometrically doubling, atom, Applied Mathematics, H-1, Metric measure space, upper doubling, Hardy space, Atom, geometrically doubling, Upper doubling, metric measure space, 515, dominating function, THEOREM, Calderón-Zygmund operator, Calderón–Zygmund operator, NON-DOUBLING MEASURES, Analysis, BMO
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