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BMO-Mappings in the Plane

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Topics in Analysis and its Applications

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry ((NAII,volume 147))

Abstract

This survey paper presents in the 2-dimensional case recent results which generalize plane quasiconformality and quasiregularity to the case of mappings whose distortion is dominated by a BMO-function. These are the so-called BMO-mappings. After a brief exposure on real BMO-functions in §2 classes of BMO-mappings are discussed in §3. §4 is devoted to BMO — QC and -QR mappings in the sense of Ryazanov, Srebro and Yakubov, and §4 to BMO-BD considered by Astala, Iwanie0107;, Koskela and Martin. BMO-mappings between Riemann and Klein surfaces are discussed in §4.5.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, Bucharest, 701091, Romania

    Cabiria Andreian Cazacu

  2. Department of Mathematics, University “Politehnica”, Splaiul Independentei 313, Bucharest 6, c. 772061

    Victoria Stanciu

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  1. Cabiria Andreian Cazacu
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  2. Victoria Stanciu
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Editors and Affiliations

  1. Institute of Mathematics of National Academy of Sciences of Armenia, Yerevan, Armenia

    G. A. Barsegian

  2. Mathematical Institute, Freie Universität Berlin, Berlin, Germany

    H. G. W. Begehr

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Cazacu, C.A., Stanciu, V. (2004). BMO-Mappings in the Plane. In: Barsegian, G.A., Begehr, H.G.W. (eds) Topics in Analysis and its Applications. NATO Science Series II: Mathematics, Physics and Chemistry, vol 147. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2128-3_2

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