For a rectifable Jordan curve Γ with complementary domainsD and D,Anderson conjectured that the Faber operator is a bounded isomorphism between the Besov spaces Bp（1 〈 p 〈 ∞） of analytic functions in the unit di...For a rectifable Jordan curve Γ with complementary domainsD and D,Anderson conjectured that the Faber operator is a bounded isomorphism between the Besov spaces Bp（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.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11071179)
文摘For a rectifable Jordan curve Γ with complementary domainsD and D,Anderson conjectured that the Faber operator is a bounded isomorphism between the Besov spaces Bp（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.
