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Differential-free Characterisation of Smooth Mappings with Controlled Growth

  • Marijan Marković (a1)

Abstract

In this paper we give some generalizations and improvements of the Pavlović result on the Holland–Walsh type characterization of the Bloch space of continuously differentiable (smooth) functions in the unit ball in ${{\text{R}}^{m}}$ .

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[1] Ahlfors, L. V., Möbius transformations in several dimensions. Ordway Professorship Lectures in Mathematics, University of Minnesota, School of Mathematics, Minneapolis, MN, 1981.
[2] Colonna, F., The Block constant of bounded harmonic mappings. Indiana Univ. Math. J. 38(1989), 829840. http://dx.doi.Org/10.1512/iumj.1989.38.38039
[3] Holland, F. and Walsh, D., Criteriafor membership of Block Space and its subspace, BMOA. Math. Ann. 273(1986), 317335. http://dx.doi.org/10.1007/BF01451410
[4] Pavlovic, M., On the Holland-Walsh characterization of Block functions. Proc. Edinb. Math. Soc. 51(2008), 439441. http://dx.doi.org/10.1017/S0013091506001076
[5] Ren, G. and Tu, C., Block Space in the unit ball of Cn. Proc. Amer. Math. Soc. 133(2005), 719726. http://dx.doi.org/10.1090/S0002-9939-04-07617-8
[6] Vuorinen, M., Conformal geometry and quasiregular mappings. Lecture Notes in Mathematics, 1319, Springer-Verlag, Berlin, 1988. http://dx.doi.Org/10.1007/BFb0077904
[7] Zhu, K., Distances and Banach Spaces of holomorphic functions on complex domains. J. London Math. Soc. 49(1994), 163182. http://dx.doi.Org/10.1112/jlms/49.1.163
[8] Zhu, K., Bloch type Spaces of analytic functions. Rocky Mountain J. Math. 23(1993), 11431177. http://dx.doi.Org/10.1216/rmjm/1181072549
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Differential-free Characterisation of Smooth Mappings with Controlled Growth

  • Marijan Marković (a1)

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