Composition operators between Hardy and weighted Bergman spaces on convex domains in $\textbf {C}^ N$
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- by Barbara D. MacCluer and Peter R. Mercer
- Proc. Amer. Math. Soc. 123 (1995), 2093-2102
- DOI: https://doi.org/10.1090/S0002-9939-1995-1254846-9
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Abstract:
Suppose $\Omega$ is a bounded, strongly convex domain in ${{\mathbf {C}}^N}$ with smooth boundary and $\phi :\Omega \to \Omega$ is an arbitrary holomorphic map. While in general the composition operator ${C_\phi }$ need not map the Hardy space ${H^p}(\Omega )$ into itself when $N > 1$, our main theorem shows that ${C_\phi }$ does map ${H^p}(\Omega )$ boundedly into a certain weighted Bergman space on $\Omega$, where the weight function depends on the dimension N. We also consider properties of ${C_\phi }$ on ${H^p}(\Omega )$ when $\phi (\Omega )$ is contained in an approach region in $\Omega$.References
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Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2093-2102
- MSC: Primary 47B38; Secondary 32A35, 46E15
- DOI: https://doi.org/10.1090/S0002-9939-1995-1254846-9
- MathSciNet review: 1254846