| For a rectifiable Jordan curve with complementary domains D and D, J. M.Anderson [2] conjectured that the Faber operator is a bounded isomorphism betweenthe Besov spaces Bp(1<p <∞) of analytic functions in the unit disk and in the innerdomain D, respectively. We point out that the conjecture is not true in the specialcase p=2, and show that in this case the Faber operator is a bounded isomorphism ifand only if Γ is a quasi-circle. |
