Composition Operators on Hardy-Orlicz Spaces, PDF eBook

Composition Operators on Hardy-Orlicz Spaces PDF

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The authors investigate composition operators on Hardy-Orlicz spaces when the Orlicz function $\Psi$ grows rapidly: compactness, weak compactness, to be $p$-summing, order bounded, $\ldots$, and show how these notions behave according to the growth of $\Psi$.

They introduce an adapted version of Carleson measure.

They construct various examples showing that their results are essentially sharp.

In the last part, they study the case of Bergman-Orlicz spaces.

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