Unbounded composition operators on 𝐻²(𝐵₂)

Cima, J. A.; Wogen, W. R.

doi:10.1090/S0002-9939-1987-0875384-4

Unbounded composition operators on $H^ 2(B_ 2)$
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by J. A. Cima and W. R. Wogen PDF

Proc. Amer. Math. Soc. 99 (1987), 477-483 Request permission

Abstract:

Examples are given of holomorphic self-maps of the unit ball on ${{\text {C}}^2}$ which induce unbounded composition operators on the Hardy space ${H^2}$. In particular, an example is given which is one-to-one on the closed ball. Also, a valence condition on the boundary of this ball is given which is sufficient for unboundedness of the induced composition operator.

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