Holomorphic Besov spaces in the polydisc and bounded Toeplitz operators

Abstract

The definition of the holomorphic, weighted Besov spaces Bp(α) in the n-dimensional polydisc is extended to all 0 < p < +∞, 1 − p < α < +∞. Then Toeplitz´ operators are sidered in Bp(α) for 1 ≤ p < ∞, and the symbols {h} for which the Toeplitz operators {Th} induce bounded operators Th : Bp(α) → Bp(α) are described. As an application, a division theorem on “good inner” functions is obtained in Bp(α).