We characterize those holomorphic mappings (?) from the polydisc Dn in Cn to itself for which the induced composition operators C(?) are bounded (or compact) from the Bloch-type space Bω to Bμ (respectively, from th...We characterize those holomorphic mappings (?) from the polydisc Dn in Cn to itself for which the induced composition operators C(?) are bounded (or compact) from the Bloch-type space Bω to Bμ (respectively, from the little Bloch-type space Bω,0 to Bμ,0), where ω is a normal function on [0,1) and μ is a nonnegative function on [0,1) with μ(tn) > 0 for some sequence {tn}n=1∞(?)[0,1) satisfying limn→∞ tn = 1.展开更多
Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we de?ne an extende...Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we de?ne an extended Ces`aro operator T_φ with the holomorphic symbol φ and characterize those φ for which T_φ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those φ for which T_φ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ. When B is the open unit ball of a ?nite dimensional complex Banach space X, this additional assumption is automatically satis?ed.展开更多
For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f...For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10471039)the Natural Science Foundation of Zhejiang Ptovince(Grant No.M103104).
文摘We characterize those holomorphic mappings (?) from the polydisc Dn in Cn to itself for which the induced composition operators C(?) are bounded (or compact) from the Bloch-type space Bω to Bμ (respectively, from the little Bloch-type space Bω,0 to Bμ,0), where ω is a normal function on [0,1) and μ is a nonnegative function on [0,1) with μ(tn) > 0 for some sequence {tn}n=1∞(?)[0,1) satisfying limn→∞ tn = 1.
基金supported by Jiangsu Natural Science fund for Colleges and Universities(06KJD110175)Natural Science Fund of Xuzhou Institute of Technology(XKY2008310)
基金supported by Japan Society for the Promotion of Science KAKENHI (Grant No. JP16K05217)
文摘Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we de?ne an extended Ces`aro operator T_φ with the holomorphic symbol φ and characterize those φ for which T_φ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those φ for which T_φ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ. When B is the open unit ball of a ?nite dimensional complex Banach space X, this additional assumption is automatically satis?ed.
文摘For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
