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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonfactorization theorems in weighted Bergman and Hardy spaces on the unit ball of $ {\bf C}\sp{n}$ $ (n>1)$


Author: M. Seetharama Gowda
Journal: Trans. Amer. Math. Soc. 277 (1983), 203-212
MSC: Primary 32A35; Secondary 46E15
MathSciNet review: 690048
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Abstract: Let $ {A^{p,\alpha }}(B),{A^{q,\alpha }}(B)$ and $ {A^{l,\alpha }}(B)$ be weighted Bergman spaces on the unit ball of $ {{\text{C}}^{n}}\,(n > 1)$. We prove:

Theorem 1. If $ 1/l = 1/p + 1/q$ then $ {A^{p,\alpha }}(B) \cdot {A^{q,\alpha }}(B)$ is of first category in $ {A^{l,\alpha }}(B)$.

Theorem 2. Theorem 1 holds for Hardy spaces in place of weighted Bergman spaces. We also show that Theorems 1 and 2 hold for the polydisc $ {U^n}$ in place of $ B$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0690048-9
PII: S 0002-9947(1983)0690048-9
Keywords: Weighted Bergman space, Hardy space, unit ball, unit polydisc
Article copyright: © Copyright 1983 American Mathematical Society



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