Besov Functions and Tangent Space to the Integrable Teichmüller Space

详细信息    查看全文 | 推荐本文 |

英文篇名：Besov Functions and Tangent Space to the Integrable Teichmüller Space 作者：Shu’an ; TANG ; Xiaogao ; FENG ; Yuliang ; SHEN 英文作者：Shu’an TANG;Xiaogao FENG;Yuliang SHEN;Department of Mathematics, Soochow University;Department of Mathematics, Guizhou Normal University;College of Mathmatics and Information, China West Normal University; 英文关键词：Universal Teichmüller space;;Integrable Teichmüller space;;Zygmund function;;Quasiconformal deformation;;Besov function 中文刊名：SXNK 英文刊名：数学年刊B辑(英文版) 机构：Department of Mathematics, Soochow University;Department of Mathematics, Guizhou Normal University;College of Mathmatics and Information, China West Normal University; 出版日期：2018-11-15 出版单位：Chinese Annals of Mathematics,Series B 年：2018 期：v.39 基金：supported by the National Natural Science Foundation of China(Nos.11371268,11171080,11601100,11701459);; the Jiangsu Provincial Natural Science Foundation of China(No.BK20141189);; the Ph.D Research Startup Foundation of Guizhou Normal University(No.11904-05032130006) 语种：英文; 页：SXNK201806004 页数：10 CN：06 ISSN：31-1329/O1 分类号：35-44

摘要

The authors identify the function space which is the tangent space to the integrable Teichm¨uller space. By means of quasiconformal deformation and an operator induced by a Zygmund function, several characterizations of this function space are obtained.
        The authors identify the function space which is the tangent space to the integrable Teichm¨uller space. By means of quasiconformal deformation and an operator induced by a Zygmund function, several characterizations of this function space are obtained.

引文

[1]Ahlfors,L.V.,Remarks on Teichm¨uller’s space of Riemann surfaces,Ann.Math.,74,1961,171-191.
    [2]Ahlfors,L.V.,Lectures on Quasiconformal Mapping,D.Van Nostrand,Princeton,New York,1966.
    [3]Ahlfors,L.V.,Quasiconformal deformations and mappings in Rn,J.Anal.Math.,30,1976,74-97.
    [4]Beurling,A.and Ahlfors,L.V.,The boundary correspondence under quasiconformal mappings,Acta Math.,96,1956,125-142.
    [5]Cui,G.,Integrably asymptotic affine homeomorphisms of the circle and Teichm¨uller spaces,Sci.China Ser.A,43,2000,267-279.
    [6]Duren,L.,Theory of Hp Spaces,Academic Press,New York,London,1970.
    [7]Gardiner,F.P.and Lakic,N.,Quasiconformal Teichm¨uller Theory,Mathematical Surveys and Monographs,76,American Mathematical Society,Providence,RI,2000.
    [8]Gardiner,F.P.and Sullivan,D.,Symmetric structure on a closed curve,Amer.J.Math.,114,1992,683-736.
    [9]Garnett,J.B.,Bounded Analytic Functions,Academic Press,New York,1981.
    [10]Guo,H.,Integrable Teichm¨uller spaces,Sci.China Ser.A,43,2000,47-58.
    [11]Hu,Y.,Song,J.,Wei,H.and Shen,Y.,An integral operator induced by a Zygmund function,J.Math.Anal.Appl.,401,2013,560-567.
    [12]Lehto,O.,Univalent Functions and Teichm¨uller Spaces,John Wiley&Sons Inc.,Springer-Verlag,New York,1986.
    [13]Nag,S.,The Complex Analytic Theory of Teichm¨uller Spaces,Wiley-Interscience,1988.
    [14]Nag,S.and Verjovsky,A.,Diff(S1)and the Teichm¨uller spaces,Comm.Math.Phys.,130,1990,123-138.
    [15]Reich,E.and Chen,J.,Extensions with bounded?-derivative,Ann.Acad.Sci.Fenn.,16,1991,377-389.
    [16]Reimann,H.,Ordinary differential equations and quasiconformal mappings,Invent.Math.,33,1976,247-270.
    [17]Shamoyan,F.A.,Toeplitz operators and division by an inner function in some spaces of analytic functions,Dokl.Akad.Nauk Armenii,76,1983,215-219.
    [18]Shen,Y.,Fourier coefficients of Zygmund functions and analytic functions with quasiconformal deformation extensions,Sci.China Math.,55,2012,607-624.
    [19]Shen,Y.,Weil-Peterssen Teichm¨uller space,Amer.J.Math.,arXiv:1304.3197.
    [20]Takhtajan,L.and Teo,L.,Weil-Petersson metric on the universal Teichm¨uller space,Mem.Amer.Math.Soc.,183(861),2006,119pp.
    [21]Tang,S.,Some characterizations of the integrable Teichm¨uller space,Sci.China Math.,56,2013,541-551.
    [22]Tang,S.and Shen,Y.,Integrable Teichm¨uller space,preprint.
    [23]Triebel,H.,Theory of Function Spaces,Monographs in Mathematics,78,Birkh¨auser,Basel,1983.
    [24]Wei,H.and Shen,Y.,On the tangent space to the BMO-Teichm¨uller space,J.Math.Anal.Appl.,419,2014,715-726.
    [25]Yanagishita,M.,Introduction of a complex structure on the p-integrable Teichm¨uller space,Ann.Acad.Sci.Fenn.Math.,39,2014,947-971.
    [26]Zhu,K.,Operator Theory in Function Spaces,Math.Surveys Monogr.,138,American Mathematical Society,Providence,RI,2007.
    [27]Zygmund,A.,Smooth functions,Duke Math.J.,12,1945,47-76.