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Compact composition operators on \(L^ 1\). (English) Zbl 0704.47018
Composition of a holomorphic function from the unit disc to itself with a Poisson integral induces a composition operator on \(L^ 1\) of the unit circle. D. Sarason recently proved that the compactness of such an operator on \(L^ 1\) implies its compactness on the Hardy space \(H^ 2\). The present paper establishes the converse.
Reviewer: E.Azoff

MSC:
47B07 Linear operators defined by compactness properties
47B38 Linear operators on function spaces (general)
30D55 \(H^p\)-classes (MSC2000)
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