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composition operator ON BERS-TYPE SPACES

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Acta Mathematica Scientia 2002年第3期22卷 404-412页

作者：何维湘姜立建 Department Of Mathemattics Helsinki University Of Technology Finland Institute of Mathematics Academia Sinica Beijing 100080 China

Necessary and sufficient conditions are established for a composition operator C(phi)f = f o phi to be bounded or compact on the Bers-type space H-alpha(infinity) and the little Bers-type space H-alpha(infinity). The boundedness and compactness of the composition operator C-phi on A(infinity)(phi) are characterized, which generalize the case of C-phi on H-alpha(infinity).

关键词： composition operator Bers-type space boundedness compactness

COLLECTIVELY COMPACT composition operator SEQUENCES BETWEEN BERGMAN AND HARDY SPACES

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Acta Mathematica Scientia 2004年第2期24卷 206-212页

作者：王茂发刘培德 SchoolofMathematicsandStatistics WuhanUniversityWuhan430072China

This paper studies the collective compactness of composition operator sequences between the Bergman and Hardy spaces. Some sufficient and necessary conditions involving the generalized Nevanlinna counting functions fo... 详细信息

关键词： Bergman space Hardy space composition operator collectively compact operator sequence

THE COMPACT composition operator ON THE μ-BERGMAN SPACE IN THE UNIT BALL

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Acta Mathematica Scientia 2017年第2期37卷 425-438页

作者：黎深莲张学军徐思 College of Mathematics and Computer Science Hunan Normal University Changsha 410006 China

Let p 〉 0 and μ be a normal function on [0, 1）, u（r） = （1 - r2）1＋n^pμ（r） for r ∈ [0, 1）. In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space AP（p） to the normal weight Bloch type space β （r）in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from A^p（μ） to βv, is given. At the same time, the authors give the briefly sufficient and necessary condition that Cv is compact on βμ, for a 〉 1.

关键词： μ-Bergman space μ-Bloch space composition operator compactness

Products of Extended Cesàro operator and composition operator from Generalized Besov Spaces to Zygmund Spaces

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Chinese Quarterly Journal of Mathematics 2012年第2期27卷 204-212页

作者： OUYANG Xiao-rong Jinxiu Middle School Hangzhou 310011 China

We characterize the boundedness and compactness of the product of extended Cesaro operator and composition operator T_gC_φ from generalized Besov spaces to Zygmund spaces,where g is a given holomorphic function in th... 详细信息

关键词： extended Ces`aro operator composition operator generalized Besov space Zygmund space

composition operators on the normal weight Dirichlet type space in the unit disc

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Frontiers of Mathematics in China 2022年第4期17卷 545-552页

作者： Xuejun ZHANG Min ZHOU Hongxin CHEN College of Mathematics and Statistics Hunan Normal UniversityChangsha410006China

Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in t... 详细信息

关键词： composition operator normal weight Dirichlet type space boundedness compactness unit disc

composition operators with Universal Translates on S^(2)(D)

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Acta Mathematica Sinica,English Series 2023年第12期39卷 2452-2464页

作者： Kai Kai HAN Yan Yan TANG School of Mathematics and Statistics Hebei University of Economics and BusinessShijiazhuang 050061P.R.China School of Mathematics and Statistics He'nan UniversityKaifeng 475004P.R.China

It is known that the Invariant Subspace Problem for Hilbert spaces is equivalent to the statement that all minimal non-trivial invariant subspaces for a universal operator are one dimensional.In this paper,we characterize all linear fractional composition operators and their adjoints that have universal translates on the space S^(2)(D).Moreover,we characterize all adjoints of linear fractional composition operators that have universal translates on the Hardy space H^(2)(D).In addition,we consider the minimal invariant subspaces of the composition operator Cφa on S^(2)(D),where φa(z)=az+1-a,a ∈(O,1).Finally,some relationships between complex symmetry and universality for bounded linear operators and commuting pairs of operators on a complex separable,infinite dimensional Hilbert space are explored.

关键词： Universal operator composition operator invariant subspace complex symmetry

JOHN-NIRENBERG-Q SPACES VIA CONGRUENT CUBES

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Acta Mathematica Scientia 2023年第2期43卷 686-718页

作者：陶金杨珍瑜袁文 Laboratory of Mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China

To shed some light on the John-Nirenberg space,the authors of this article introduce the John-Nirenberg-Q space via congruent cubes,JNQp,qα(Rn),which,when p=∞and q=2,coincides with the space Qα(Rn)introduced by Essen,Janson,Peng and Xiao in[Indiana Univ Math J,2000,49(2):575-615].Moreover,the authors show that,for some particular indices,JNQp,qα(Rn)coincides with the congruent John-Nirenberg space,or that the(fractional)Sobolev space is continuously embedded into JNQp,qα(Rn).Furthermore,the authors characterize JNQp,qα(Rn)via mean oscillations,and then use this characterization to study the dyadic counterparts.Also,the authors obtain some properties of composition operators on such spaces.The main novelties of this article are twofold:establishing a general equivalence principle for a kind of’almost increasing’set function that is here introduced,and using the fine geometrical properties of dyadic cubes to properly classify any collection of cubes with pairwise disjoint interiors and equal edge length.

关键词： John-Nirenberg space congruent cube Q space (fractional)Sobolev space mean oscillation dyadic cube composition operator

composition operators on α-Bloch Spaces of the Unit Ball

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Acta Mathematica Sinica,English Series 2007年第11期23卷 1991-2002页

作者： Min Zhu ZHANG Wen XU Department of Mathematics Nanjing Normal University Nanjing 210097 P. R. China Department of Mathematics Southeast University Nanjing 210096 P. R. China Department of Physics and Mathematics University of Joensuu Fin-80101 Joensuu Finland

The authors characterize the boundedness and compactness of composition operators between α-Bloch spaces of the unit ball.

关键词： α-Bloch space composition operator boundedness compactness

THE PRODUCT operator BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

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Acta Mathematica Scientia 2021年第5期41卷 1606-1618页

作者：梁玉霞 School of Mathematical Sciences Tianjin Normal UniversityTianjin 300387China

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.

关键词： essential norm differentiation composition operator Bloch-type space slice regular functions