Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces.The Grunsky map is known to be holomorphic on the universal Teichmüller space.In this pa...Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces.The Grunsky map is known to be holomorphic on the universal Teichmüller space.In this paper the authors deal with the compactness of a Grunsky differential operator.They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.展开更多
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the National Natural Science Foundation of China(No.11631010)。
文摘Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces.The Grunsky map is known to be holomorphic on the universal Teichmüller space.In this paper the authors deal with the compactness of a Grunsky differential operator.They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator.
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.
