On boundedness of composition operators on 𝐻²(𝐵₂)

Cima, Joseph A.; Stanton, Charles S.; Wogen, Warren R.

doi:10.1090/S0002-9939-1984-0740174-7

On boundedness of composition operators on $H\sp{2}(B\sb{2})$

Authors: Joseph A. Cima, Charles S. Stanton and Warren R. Wogen
Journal: Proc. Amer. Math. Soc. 91 (1984), 217-222
MSC: Primary 47B37; Secondary 32A35
DOI: https://doi.org/10.1090/S0002-9939-1984-0740174-7
MathSciNet review: 740174
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Abstract: Composition operators on the Hardy space ${H^2}$ of the ball in ${C^2}$ are studied. Some sufficient conditions are given for a composition operator to be bounded. A class of inner mappings is given which induces isometric composition operators. Another class of inner mappings is shown to induce unbounded composition operators.

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