Composition Operator on Bergman-Orlicz Space
نویسندگان
چکیده
منابع مشابه
Composition Operator on Bergman-Orlicz Space
Recommended by Shusen Ding Let D denote the open unit disk in the complex plane and let dAz denote the normalized area measure on D. Φ α is defined as follows L Φ α {f ∈ HD : D ΦΦlog |fz|1 − |z| 2 α dAz < ∞}. Let ϕ be an analytic self-map of D. The composition operator C ϕ induced by ϕ is defined by C ϕ f f • ϕ for f analytic in D. We prove that the composition operator C ϕ is compact on L Φ α ...
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and Applied Analysis 3 2. Main Results and Proofs Lemma 2.1. For α α1, . . . , αn ∈ D, let uα z1, . . . , zn ∏n j 1 1 − |αj |2 / 1 − αjzj . Then uα z1, . . . , zn ∈ Lφa D , and ‖uα z ‖σn ≤ 1 φ−1 ∏n j 1 ( 1/δ2 j )) . 2.1 Proof. It is easy to see that ‖uα z ‖∞ ∏n j 1 1 |αj | / 1 − |αj | 2 ∏n j 1 2 − δj /δj . Since φ 0 0, the convexity of φ implies φ ax ≤ aφ x for 0 ≤ a ≤ 1. Hence, for every C > 0...
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Let D= {z ∈ C : |z| < 1} be the open unit disk in the complex plane C. Let A2(D) be the space of analytic functions on D square integrable with respect to the measure dA(z) = (1/π)dx dy. Given a ∈D and f any measurable function on D, we define the function Ca f by Ca f (z) = f (φa(z)), where φa ∈ Aut(D). The map Ca is a composition operator on L2(D,dA) and A2(D) for all a ∈D. Let (A2(D)) be the...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2009
ISSN: 1029-242X
DOI: 10.1155/2009/832686