We employ a new reverse Carleson type condition and define a new sampling condition to study closed range composition operators on BMOA. We provide necessary and also sufficient conditions for a composition operator to be closed range on BMOA. We show that a composition operator is closed range as an operator from the Bloch space to BMOA if and only if it is bounded below on all Möbius transformations.

中文翻译：

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BMOA上的近距离合成算子

我们采用了一种新的反向Carleson型条件，并定义了一个新的采样条件，以研究BMOA上的近距离合成算符。我们提供了必要和充分的条件，使合成算子在BMOA上处于封闭范围。我们证明，当且仅当在所有Möbius变换上都限于下限时，构图算子是从Bloch空间到BMOA的算子的封闭范围。