In this paper,we give a survey of some recent progress in terms of verifying Carleson measures;this includes the difference between two definitions of a Carleson measure,the Bergman tree condition,the T1 condition for...In this paper,we give a survey of some recent progress in terms of verifying Carleson measures;this includes the difference between two definitions of a Carleson measure,the Bergman tree condition,the T1 condition for Besov-Sobolev spaces on a complex ball,vector-valued Carleson measures,Carleson measures in strongly pseudoconvex domains and reverse Carleson measures.展开更多
Let F = {f} be a family of entire functions and f(k) the k-th derivative of f. The author studies the relation of the nomality of F and that of {f(k) o f : f ∈F} or {f o f(k):f∈F}.
This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, B...This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）展开更多
In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized,...In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.展开更多
In this paper, we discuss the Valiron＇s theorem in the unit polydisk D^N. We prove that for a holomorphic map φ：D^N→D^N satisfying some regular conditions, there exists a holomorphic map θ：D^N→H and a constant...In this paper, we discuss the Valiron＇s theorem in the unit polydisk D^N. We prove that for a holomorphic map φ：D^N→D^N satisfying some regular conditions, there exists a holomorphic map θ：D^N→H and a constant α〉 0 such that θ°φ=1/αθ. It is based on the extension of Julia-Wolff-Caratheodory （JWC） theorem of D in the polydisk.展开更多
Let D be the unit disc and H（D） be the set of all analytic functions on D. In [2], C. Cowen defined a space H = f ∈ H（D） ： f（z） =sum from k=o to ∞ ak（z ＋ 1）k, z ∈ D, ‖f‖2 = sum from k=o to ∞ ｜ak｜24k ...Let D be the unit disc and H（D） be the set of all analytic functions on D. In [2], C. Cowen defined a space H = f ∈ H（D） ： f（z） =sum from k=o to ∞ ak（z ＋ 1）k, z ∈ D, ‖f‖2 = sum from k=o to ∞ ｜ak｜24k ∞In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.展开更多
文摘In this paper,the Nevanlinna direction, Borel direction and exceptional value of quasimeromorphic mapping are discussed and some results are obtained.
基金Supported by the National Natural Science Foundation of China(11771441,11601400)。
文摘In this paper,we give a survey of some recent progress in terms of verifying Carleson measures;this includes the difference between two definitions of a Carleson measure,the Bergman tree condition,the T1 condition for Besov-Sobolev spaces on a complex ball,vector-valued Carleson measures,Carleson measures in strongly pseudoconvex domains and reverse Carleson measures.
文摘Let F = {f} be a family of entire functions and f(k) the k-th derivative of f. The author studies the relation of the nomality of F and that of {f(k) o f : f ∈F} or {f o f(k):f∈F}.
基金Supported in part by the National Natural Science Foundation of China(11271359)the Fundamental Research Funds for the Central Universities(2014-Ia-037and 2015-IVA-069)
文摘This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）
基金partially supported by NSFC(11771340,11701434,11431011,11471251,11771441)
文摘In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.
基金Supported by the National Natural Science Foundation of China(11271359)
文摘In this paper, we discuss the Valiron＇s theorem in the unit polydisk D^N. We prove that for a holomorphic map φ：D^N→D^N satisfying some regular conditions, there exists a holomorphic map θ：D^N→H and a constant α〉 0 such that θ°φ=1/αθ. It is based on the extension of Julia-Wolff-Caratheodory （JWC） theorem of D in the polydisk.
基金Supported in part by the National Natural Science Foundation of China (10901158)
文摘Let D be the unit disc and H（D） be the set of all analytic functions on D. In [2], C. Cowen defined a space H = f ∈ H（D） ： f（z） =sum from k=o to ∞ ak（z ＋ 1）k, z ∈ D, ‖f‖2 = sum from k=o to ∞ ｜ak｜24k ∞In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.
