After reviewing Grunsky operator and Faber operator acting on Dirichlet space,we discuss the boundedness of Faber operator on BMOA,a new subject which turns out to be closely related to the BMO theory of the universal...After reviewing Grunsky operator and Faber operator acting on Dirichlet space,we discuss the boundedness of Faber operator on BMOA,a new subject which turns out to be closely related to the BMO theory of the universal Teichmüller space.In particular,we show that the Faber operator acts as a bounded operator on BMOA if the symbol conformal map stays nearly to the base point in the BMO-Teichmüller space.Meanwhile,we obtain several results on quasiconformal mappings,BMOTeichm¨uller space and chord-arc curves as well.As by-products,this provides a complex analysis approach to the boundedness of the Cauchy integral acting on BMO functions on a chord-arc curve near to the unit circle in the BMO-Teichmüller space.展开更多
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
We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obt...We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions.展开更多
文摘After reviewing Grunsky operator and Faber operator acting on Dirichlet space,we discuss the boundedness of Faber operator on BMOA,a new subject which turns out to be closely related to the BMO theory of the universal Teichmüller space.In particular,we show that the Faber operator acts as a bounded operator on BMOA if the symbol conformal map stays nearly to the base point in the BMO-Teichmüller space.Meanwhile,we obtain several results on quasiconformal mappings,BMOTeichm¨uller space and chord-arc curves as well.As by-products,this provides a complex analysis approach to the boundedness of the Cauchy integral acting on BMO functions on a chord-arc curve near to the unit circle in the BMO-Teichmüller space.
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.
基金supported by the Program for New Century Excellent Talents in University (Grant No. 06-0504)National Natural Science Foundation of China (Grant No. 10771153)
文摘We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions.
