We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that c...We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that compactness of a composition operator on BMOA implies its compactness on the Bloch space as well as on the Hardy space.Similar results on VMOA are also given.展开更多
1984年Svate,Janson等人证明了Hankel算子H■(f∈H^(2)(D))在H^(2)(D)上有界的充要条件是f∈BMOA=(H^(1))^(*)。H■在H^(2)(D)上是紧算子的充要条件是f∈VMOA=the predual of H^(1)(D)。1986年Bonsall证明了Hankel算子H■(f∈L_(a)^(2)(...1984年Svate,Janson等人证明了Hankel算子H■(f∈H^(2)(D))在H^(2)(D)上有界的充要条件是f∈BMOA=(H^(1))^(*)。H■在H^(2)(D)上是紧算子的充要条件是f∈VMOA=the predual of H^(1)(D)。1986年Bonsall证明了Hankel算子H■(f∈L_(a)^(2)(D))在L_(a)^(2)(D)上有界的充要条件是f∈Bloch=(L_(a)^(1)(D))^(*)。展开更多
We study the weighted composition operators Wh,on Hardy space H2（B） whenever h ∈ BMOA（resp.h ∈ VMOA）.Analogous results are given for Hp（B） spaces and the scale of weighted Bergman spaces.In the latter case,BMO...We study the weighted composition operators Wh,on Hardy space H2（B） whenever h ∈ BMOA（resp.h ∈ VMOA）.Analogous results are given for Hp（B） spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space（resp.VMOA by the little Bloch space）.展开更多
基金This work was partially supported by the Research Foundation for Doctor Programme(Grant No.20060560002)the National Natural Science Foundation of China(Grant No.10671115)
文摘We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that compactness of a composition operator on BMOA implies its compactness on the Bloch space as well as on the Hardy space.Similar results on VMOA are also given.
文摘1984年Svate,Janson等人证明了Hankel算子H■(f∈H^(2)(D))在H^(2)(D)上有界的充要条件是f∈BMOA=(H^(1))^(*)。H■在H^(2)(D)上是紧算子的充要条件是f∈VMOA=the predual of H^(1)(D)。1986年Bonsall证明了Hankel算子H■(f∈L_(a)^(2)(D))在L_(a)^(2)(D)上有界的充要条件是f∈Bloch=(L_(a)^(1)(D))^(*)。
基金Supported by National Natural Science Foundation of China(Grant No.10971040)
文摘We study the weighted composition operators Wh,on Hardy space H2（B） whenever h ∈ BMOA（resp.h ∈ VMOA）.Analogous results are given for Hp（B） spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space（resp.VMOA by the little Bloch space）.
