让 B 是在一个复杂 Banach 空格的联合起来的球。让 S <SUB > k+1 </SUB><SUP>*</SUP>(B) 是 B 上的规范的星形的地图砰 f 的家庭以便 0 是的 z = f (z)-z 的零顺序 k+1。作者突然地获得生长和盖住的定理，以...让 B 是在一个复杂 Banach 空格的联合起来的球。让 S <SUB > k+1 </SUB><SUP>*</SUP>(B) 是 B 上的规范的星形的地图砰 f 的家庭以便 0 是的 z = f (z)-z 的零顺序 k+1。作者突然地获得生长和盖住的定理，以及锋利的系数为 S <SUB 的各种各样的子集跳 > k+1 </SUB><SUP>*</SUP>(B) 。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
In this paper,we study some extremal problems for the family Sg^0(BX)of normalized univalent mappings with g-parametric representation on the unit ball BX of an n-dimensional JB*-triple X with r≥2,where r is the rank...In this paper,we study some extremal problems for the family Sg^0(BX)of normalized univalent mappings with g-parametric representation on the unit ball BX of an n-dimensional JB*-triple X with r≥2,where r is the rank of X and g is a convex(univalent)function on the unit disc U,which satisfies some natural assumptions.We obtain sharp coefficient bounds for the family Sg^0(BX),and examples of bounded support points for various subsets of Sg^0(BX).Our results are generalizations to bounded symmetric domains of known recent results related to support points for families of univalent mappings on the Euclidean unit ball B^n and the unit polydisc U^n in C^n.Certain questions will be also mentioned.Finally,we point out sharp coefficient bounds and bounded support points for the family Sg^0(B^n)and for special compact subsets of Sg^0(B^n),in the case n≥2.展开更多
基金Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (Nos.19540205,200717540138,2007).
文摘让 B 是在一个复杂 Banach 空格的联合起来的球。让 S <SUB > k+1 </SUB><SUP>*</SUP>(B) 是 B 上的规范的星形的地图砰 f 的家庭以便 0 是的 z = f (z)-z 的零顺序 k+1。作者突然地获得生长和盖住的定理，以及锋利的系数为 S <SUB 的各种各样的子集跳 > k+1 </SUB><SUP>*</SUP>(B) 。
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.
基金supported by Japan Society for the Promotion of Science KAKENHI(Grant No.JP19K03553)。
文摘In this paper,we study some extremal problems for the family Sg^0(BX)of normalized univalent mappings with g-parametric representation on the unit ball BX of an n-dimensional JB*-triple X with r≥2,where r is the rank of X and g is a convex(univalent)function on the unit disc U,which satisfies some natural assumptions.We obtain sharp coefficient bounds for the family Sg^0(BX),and examples of bounded support points for various subsets of Sg^0(BX).Our results are generalizations to bounded symmetric domains of known recent results related to support points for families of univalent mappings on the Euclidean unit ball B^n and the unit polydisc U^n in C^n.Certain questions will be also mentioned.Finally,we point out sharp coefficient bounds and bounded support points for the family Sg^0(B^n)and for special compact subsets of Sg^0(B^n),in the case n≥2.
