Abstract
For a rectifiable Jordan curve Γ with complementary domains D and D*, Anderson conjectured that the Faber operator is a bounded isomorphism between the Besov spaces B p (1 < p < ∞) of analytic functions in the unit disk and in the inner domain D, respectively. We point out that the conjecture is not true in the special case p = 2, and show that in this case the Faber operator is a bounded isomorphism if and only if Γ is a quasi-circle.
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