# zbMATH — the first resource for mathematics

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)
Full Text: