Holomorphic Besov spaces in the polydisc and bounded Toeplitz operators

✍ Scribed by Harutyunyan, Anahit V.; Harutyunyan, Gohar

• Book ID: 120809513
• Publisher: Oldenbourg Wissenschaftsverlag
• Year: 2010
• Tongue: English
• Weight: 148 KB
• Volume: 30
• Category: Article
• ISSN: 0174-4747
• DOI: 10.1524/anly.2010.1023

✦ Synopsis

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 (α) → B p (α) are described. As an application, a division theorem on "good inner" functions is obtained in B p (α).