复合算子在泛函分析与算子理论当中有丰富的应用与深厚的研究背景,在泛函分析中,人们关注各种函数空间的性质与结构,如Lp空间和连续函数空间C(X)等。复合函数作为一种将函数空间进行变换的工具,有助于深入理解函数空间之间的关系与结构...复合算子在泛函分析与算子理论当中有丰富的应用与深厚的研究背景,在泛函分析中,人们关注各种函数空间的性质与结构,如Lp空间和连续函数空间C(X)等。复合函数作为一种将函数空间进行变换的工具,有助于深入理解函数空间之间的关系与结构,例如通过研究复合算子在不同函数空间上的作用,可以揭示函数空间的嵌入性、紧性以及有界性等等。不仅如此,复合算子在动力系统与遍历理论、量子力学、算子代数等数学分支当中也作为算子论的工具,推动其他数学分支的发展。而超复合算子是指以整函数作为复合子的特殊复合算子,推动着算子论的发展:超复合算子的有界性是研究复合算子当中比较重要的部分。近年来,有许多学者研究了超复合算子作用在一些经典的解析函数空间上的有界性。本文通过利用Zp空间的定义与性质,讨论了超复合算子上Bloch-type空间Bα到Zp空间的有界性问题以及Bloch-type空间Bα到Morrey空间上的有界性问题。Composite operators have extensive applications and a profound research background in functional analysis and operator theory. In functional analysis, researchers focus on the properties and structures of various function spaces, such as Lpspaces and the continuous function space C(X). As a tool for transforming function spaces, composite operators contribute to a deeper understanding of the relationships and structures among function spaces. For instance, by studying the actions of composite operators on different function spaces, one can reveal properties like the embedding, compactness, and boundedness of function spaces. Moreover, composite operators as tools in operator theory, also play a role in promoting the development of other mathematical branches, such as dynamical systems and ergodic theory, quantum mechanics, and operator algebras. Superposite operators are special composite operators with entire functions as the composition elements, and they also drive the development of operator theory. The boundedness of Superposite operators is a crucial part of the study of composite operators. In recent years, many scholars have investigated the boundedness of Superposite operators acting on some classical analytic function spaces. This paper, by making use of the definitions and properties of Zpspaces, derives the boundedness problem of Superposite operators from the Bloch-type space Bαto the Zpspace and Bloch-type space Bαto Morrey space.展开更多
This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt...This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).展开更多
The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an ...The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an operator from Bω to Bμ is denoted by ｜｜Tφ｜｜e,Bω→Bμ. The purpose of this paper is to prove that, for w, ω normal and φ ∈ H（B）｜｜Tφ｜｜e,Bω→Bμ≈lim sup｜z｜→1μ（z）｜Rφ（z）｜∫0^｜z｜dt/ω（t）.展开更多
The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,...Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.展开更多
There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of th...There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.展开更多
In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another ...In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.展开更多
In this paper, we obtain the exact norm of a class of singular integral operators Qα, α 〉 0, defined by Qαf（z） = α∫D（f（w）/（1-zw）（α＋1））dA（w）,from L∞（D） onto Bloch-type space Bα over the unit dis...In this paper, we obtain the exact norm of a class of singular integral operators Qα, α 〉 0, defined by Qαf（z） = α∫D（f（w）/（1-zw）（α＋1））dA（w）,from L∞（D） onto Bloch-type space Bα over the unit disk D, which is an extension of the Bergman projection P. We also consider the norm for this operator from C（D） onto the little Bloch-type space B（α,0）.展开更多
In this paper,we study the boundedness of an integral operator K over the unit disk D,defined as Kf(z)=∫_(D)f(w)/1-zwdA(w),which can be viewed as a cousin of the classical Bergman projection,and we establish satisfac...In this paper,we study the boundedness of an integral operator K over the unit disk D,defined as Kf(z)=∫_(D)f(w)/1-zwdA(w),which can be viewed as a cousin of the classical Bergman projection,and we establish satisfactory boundedness results between Bloch-type spaces,H^(∞)and L^(p) spaces.展开更多
We characterize the symbol for which the induced extended Cesàro operator T: Bω→ Bμ(respectively, Bω,0 → Bμ,0) is bounded or compact, where is a given holomorphic function on the unit disc D, ω and...We characterize the symbol for which the induced extended Cesàro operator T: Bω→ Bμ(respectively, Bω,0 → Bμ,0) is bounded or compact, where is a given holomorphic function on the unit disc D, ω and μ both are normal functions on [0,1).展开更多
The aim of this paper is to explore the equivalent characterizations for the boundedness and compactness of C_(φ)-C_(ψ)acting from classical(little)Zygmund space Z(Z_(0))to(little)Bloch-type space B^(α)(B_(0)^(α))...The aim of this paper is to explore the equivalent characterizations for the boundedness and compactness of C_(φ)-C_(ψ)acting from classical(little)Zygmund space Z(Z_(0))to(little)Bloch-type space B^(α)(B_(0)^(α)).Especially,we creatively develop a useful lemma,which not only plays a crucial role in the estimations but also offers a sufficient condition for the bounded below property of composition operators.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
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
文摘复合算子在泛函分析与算子理论当中有丰富的应用与深厚的研究背景,在泛函分析中,人们关注各种函数空间的性质与结构,如Lp空间和连续函数空间C(X)等。复合函数作为一种将函数空间进行变换的工具,有助于深入理解函数空间之间的关系与结构,例如通过研究复合算子在不同函数空间上的作用,可以揭示函数空间的嵌入性、紧性以及有界性等等。不仅如此,复合算子在动力系统与遍历理论、量子力学、算子代数等数学分支当中也作为算子论的工具,推动其他数学分支的发展。而超复合算子是指以整函数作为复合子的特殊复合算子,推动着算子论的发展:超复合算子的有界性是研究复合算子当中比较重要的部分。近年来,有许多学者研究了超复合算子作用在一些经典的解析函数空间上的有界性。本文通过利用Zp空间的定义与性质,讨论了超复合算子上Bloch-type空间Bα到Zp空间的有界性问题以及Bloch-type空间Bα到Morrey空间上的有界性问题。Composite operators have extensive applications and a profound research background in functional analysis and operator theory. In functional analysis, researchers focus on the properties and structures of various function spaces, such as Lpspaces and the continuous function space C(X). As a tool for transforming function spaces, composite operators contribute to a deeper understanding of the relationships and structures among function spaces. For instance, by studying the actions of composite operators on different function spaces, one can reveal properties like the embedding, compactness, and boundedness of function spaces. Moreover, composite operators as tools in operator theory, also play a role in promoting the development of other mathematical branches, such as dynamical systems and ergodic theory, quantum mechanics, and operator algebras. Superposite operators are special composite operators with entire functions as the composition elements, and they also drive the development of operator theory. The boundedness of Superposite operators is a crucial part of the study of composite operators. In recent years, many scholars have investigated the boundedness of Superposite operators acting on some classical analytic function spaces. This paper, by making use of the definitions and properties of Zpspaces, derives the boundedness problem of Superposite operators from the Bloch-type space Bαto the Zpspace and Bloch-type space Bαto Morrey space.
基金Supported by the NNSF of China(10771064, 11101139)Supported by the NSF of Zhejiang Province(Y7080197, Y6090036, Y6100219)Supported by the Foundation of Creative Group in Colleges and Universities of Zhejiang Province(T200924)
文摘This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).
基金Supported by the NNSF of China（10771064） Supported by the Natural Science Foundation of Zhejiang Province（YT080197, Y6090036, Y6100219） Supported by the Foundation of Creative Group in Colleges and Universities of Zhejiang Province（T200924） Acknowledgement The author would like to express her thanks to her supervisor, Prof HU Zhang-jian, for his guidance.
文摘The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an operator from Bω to Bμ is denoted by ｜｜Tφ｜｜e,Bω→Bμ. The purpose of this paper is to prove that, for w, ω normal and φ ∈ H（B）｜｜Tφ｜｜e,Bω→Bμ≈lim sup｜z｜→1μ（z）｜Rφ（z）｜∫0^｜z｜dt/ω（t）.
基金item： Supported by the National Natural Science Foundation of China（60573040）
文摘The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
基金Supported by the NNSF of China (10771064,10971063)the NSF of Zhejiang Province (Y6100219, Y7080197, Y6090036, D7080080)the Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924)
文摘Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.
基金supported by the National Natural Science Foundation of China(11701422).
文摘There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.
基金Supported by National Natural Science Foundation of China (No.10971153)
文摘In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.
基金Supported by the Natural Science Foundation of Zhejiang Province(Grant No.LY14A010021)
文摘In this paper, we obtain the exact norm of a class of singular integral operators Qα, α 〉 0, defined by Qαf（z） = α∫D（f（w）/（1-zw）（α＋1））dA（w）,from L∞（D） onto Bloch-type space Bα over the unit disk D, which is an extension of the Bergman projection P. We also consider the norm for this operator from C（D） onto the little Bloch-type space B（α,0）.
基金Supported by the Natural Science Foundation of Zhejiang Province(Grant No.LY14A010021)。
文摘In this paper,we study the boundedness of an integral operator K over the unit disk D,defined as Kf(z)=∫_(D)f(w)/1-zwdA(w),which can be viewed as a cousin of the classical Bergman projection,and we establish satisfactory boundedness results between Bloch-type spaces,H^(∞)and L^(p) spaces.
基金Supported by the National Natural Science Foundation of China(10471039)Supported by the Natural Science Foundation of Zhejiang Province(Y606197)Supported by the Foundation of Education of Zhejiang Province(20070482)
文摘We characterize the symbol for which the induced extended Cesàro operator T: Bω→ Bμ(respectively, Bω,0 → Bμ,0) is bounded or compact, where is a given holomorphic function on the unit disc D, ω and μ both are normal functions on [0,1).
基金supported by the National Natural Science Foundations of China(Grant No.12471126)supported by the Natural Science Foundation of Hebei Province(Grant No.A2023202031)。
文摘The aim of this paper is to explore the equivalent characterizations for the boundedness and compactness of C_(φ)-C_(ψ)acting from classical(little)Zygmund space Z(Z_(0))to(little)Bloch-type space B^(α)(B_(0)^(α)).Especially,we creatively develop a useful lemma,which not only plays a crucial role in the estimations but also offers a sufficient condition for the bounded below property of composition operators.
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 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.
