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carleson measure Characterization of Bloch Functions

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Acta Mathematica Sinica,English Series 1996年第2期12卷 175-184页

作者： Lou Zengjian Lou Zengjian Department of Mathematics Qufu Normal University Qufu,273165 China and Institute of Mathematics Academia Sinica Beijing,100080 China e-mail:Ijlou@***

We give several equivalences of Bloch functions and little Bloch *** these results we obtain the generalized carleson measure characterization of Bloch functions and the generalized vanishing carleson measure characterization of little Bloch functions,that is,f ∈ B if and only if |Dβf（z）|p（1-|z|2）βp-1dm（z）is a generalized carleson measure; f ∈ B0 if and only if |Dβf（z）|p（1-|z|2）βp-1dm（z）is a generalized vanishing carleson measure,where Dβf（β>0）is the fractional derivative of analytic function f of order β,m denotes the normalised Lebesgue measure.

关键词： Bloch space carleson measure Generalized carleson measure

α-carleson measure AND BLOCH FUNCTIONS ON BOUNDED SYMMETRIC DOMAINS OF C^n

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Acta Mathematica Scientia 1995年第4期15卷 385-393页

作者：欧阳才衡 Wuhan Inst. of Math. Sci. Chinese Acad. of Sci. Wuhan 430071 China

In this paper we defineα-carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.

关键词： carleson measure Bloch functions bounded symmetric domains.

Toeplitz Operators and carleson measures for Weighted Bergman Spaces Induced by Regular Weights

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1345-1359页

作者： Jun Tao DU Song Xiao Hasi WULAN Department of Mathematics Guangdong University of Petrochemical TechnologyMaoming 525000P.R.China Department of Mathematics Shantou UniversityShantou 515063P.R.China

In this paper,we give a universal description of the boundedness and compactness of Toeplitz operator T_(μ)^(ω)between Bergman spaces A_(η)^(p)and A_(υ)^(q)whenμis a positive Borel measure,1 详细信息

关键词： Bergman space carleson measure Toeplitz operator regular weight

A DERIVATIVE-HILBERT OPERATOR ACTING FROM LOGARITHMIC BLOCH SPACES TO BERGMAN SPACES

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Acta Mathematica Scientia 2024年第5期44卷 1916-1930页

作者： Shanli YE Yun XU School of Science Zhejiang University of Science and TechnologyHangzhou310023China

Letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entriesμn,k=μn+k,whereμn=⨜[0,1)tndμ(t),induces,formally,the operator■where■is an analytic function *** characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the Bergman space■,where 0≤αmeasuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the classical Bloch space■.

关键词： derivative-Hilbert operator logarithmic Bloch space carleson measure

TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE

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Acta Mathematica Scientia 2024年第5期44卷 1707-1720页

作者： Lixia FENG Yan LI Zhiyu WANG Liankuo ZHAO School of Mathematics and Computer Science Shanxi Normal UniversityTaiyuan030031China

In this paper,by characterizing carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.

关键词： weighted Bergman spaces Békolléweights carleson measure Toeplitz operators

ON QK（p）-TEICHMüLLER SPACES

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Acta Mathematica Scientia 2024年第6期44卷 2283-2295页

作者：漆毅吴艳 School of Mathematical Sciences Beihang University School of Mathematics and Statistics Linyi University

The QK（p）-Teichmüller space is introduced and studied in this *** characterizations of the QK（p）-Teichmüller space and the QK,0（p）-Teichmüller space are *** Schwarzian derivative model and pre-logarithmic der... 详细信息

关键词： 30C62 30F60 30H25 carleson measure pre-logarithmic derivative QK(p, q) spaces Schwarzian derivative universal Teichmüller space

carleson measures on Planar Sets

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Acta Mathematica Sinica,English Series 2009年第11期25卷 1881-1892页

作者： Zhijian QIU School of Mathematics,Southwestern University of Finance and Economics,Chengdu 610074,P. R. China School of Mathematics Southwestern University of Finance and Economics Chengdu P. R. China

In this paper, we investigate what are carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on δW. We characterize all carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of carleson measures probably is up to this class of open subsets

关键词： carleson measure circular domain harmonic measure multi-nicely connected domain

carleson measures on the Weighted Bergman Spaces with Békollé Weights

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Chinese Annals of Mathematics,Series B 2021年第4期42卷 583-600页

作者： Cezhong TONG Junfeng LI Institute of Mathematics Hebei University of TechnologyTianjin 300401China Depaxtment of Mathematical Sciences Tsinghua UniversityBeijing 100084China

In this paper,the authors characterize carleson measures for the weighted Bergman spaces with Békollé weights on the unit *** apply the carleson embedding theorem to study the properties of Toeplitz-type operators a... 详细信息

关键词： Békolléweight Bergman space carleson measure Toeplitz operator Composition operator

D_(K) SPACES AND carleson measureS

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Acta Mathematica Scientia 2022年第3期42卷 1103-1112页

作者： Dongxing LI Hasi WULAN Ruhan ZHAO School of Financial Mathematics and Statistics Guangdong University of FinanceGuangzhou 510521China Department of Mathematics Shantou UniversityShantou 515063China Department of Mathematics SUNY BrockportBrockportNY 14420USA

We give some characterizations of carleson measures for Dirichlet type spaces by using Hadamard *** also give a one-box condition for such carleson measures.

关键词： DK space Hadamard product mean growth carleson measure