Composition operators on weighted Bergman spaces of a half-plane
2011 ◽
Vol 54
(2)
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pp. 373-379
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AbstractWe use induction and interpolation techniques to prove that a composition operator induced by a map ϕ is bounded on the weighted Bergman space $\mathcal{A}^2_\alpha(\mathbb{H})$ of the right half-plane if and only if ϕ fixes the point at ∞ non-tangentially and if it has a finite angular derivative λ there. We further prove that in this case the norm, the essential norm and the spectral radius of the operator are all equal and are given by λ(2+α)/2.
2018 ◽
Vol 107
(02)
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pp. 199-214
Keyword(s):
2017 ◽
Vol 447
(2)
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pp. 817-833
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Keyword(s):
2009 ◽
Vol 7
(3)
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pp. 225-240
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2008 ◽
Vol 77
(1)
◽
pp. 161-165
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Keyword(s):
Keyword(s):