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A Norm on the Holomorphic Besov Space

✍ Scribed by Bjarte Böe


Book ID
120809518
Publisher
American Mathematical Society
Year
2003
Tongue
English
Weight
503 KB
Volume
131
Category
Article
ISSN
0002-9939

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✍ Harutyunyan, Anahit V.; Lusky, Wolfgang 📂 Article 📅 2010 🏛 Oldenbourg Wissenschaftsverlag 🌐 English ⚖ 133 KB

In this work we introduce ω-weighted Besov spaces of holomorphic functions on the polydisc in the case if 0 < p < 1. We describe the holomorphic Besov space in terms of the corresponding L p (ω) space. The projection theorems and theorems of the existence of inverse are proved. This work gives also

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The definition of the holomorphic, weighted Besov spaces B p (α) in the n-dimensional polydisc is extended to all 0 < p < +∞, 1p < α < +∞. Then Toeplitz' operators are considered in B p (α) for 1 ≤ p < ∞, and the symbols {h} for which the Toeplitz operators {T h } induce bounded operators T h : B p