Boundedness of θ-type Calderón-Zygmund operators on non-homogeneous metric measure space

Abstract

Let (X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hytönen. Under this assumption, we prove thatθ-type Calderón-Zygmund operators which are bounded on L²(μ) are also bounded from L^∞(μ) into RBMO(μ) and from H^1,∞_at (μ) into L¹(μ).

Keywords

Non-homogeneous spaces / θ-type Calderón-Zygmund operators / RBMO(μ) space / H¹ / ^,∞_at (μ) space

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Higher Education Press and Springer-Verlag Berlin Heidelberg