Geodesic
Differential-free Characterisation of Smooth Mappings with Controlled Growth
Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 628-636

Voir la notice de l'article provenant de la source Cambridge University Press

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 ${{\text{R}}^{m}}$ .
DOI : 10.4153/CMB-2017-051-7
Mots-clés : 32A18, 30D45, Bloch type spaces, Lipschitz type spaces, Holland-Walsh characterisation, hyperbolic distance, analytic function, Möbius transform 
Marković, Marijan. Differential-free Characterisation of Smooth Mappings with Controlled Growth. Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 628-636. doi: 10.4153/CMB-2017-051-7
@article{10_4153_CMB_2017_051_7,
     author = {Markovi\'c, Marijan},
     title = {Differential-free {Characterisation} of {Smooth} {Mappings} with {Controlled} {Growth}},
     journal = {Canadian mathematical bulletin},
     pages = {628--636},
     year = {2018},
     volume = {61},
     number = {3},
     doi = {10.4153/CMB-2017-051-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-051-7/}
}
TY  - JOUR
AU  - Marković, Marijan
TI  - Differential-free Characterisation of Smooth Mappings with Controlled Growth
JO  - Canadian mathematical bulletin
PY  - 2018
SP  - 628
EP  - 636
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-051-7/
DO  - 10.4153/CMB-2017-051-7
ID  - 10_4153_CMB_2017_051_7
ER  - 
%0 Journal Article
%A Marković, Marijan
%T Differential-free Characterisation of Smooth Mappings with Controlled Growth
%J Canadian mathematical bulletin
%D 2018
%P 628-636
%V 61
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-051-7/
%R 10.4153/CMB-2017-051-7
%F 10_4153_CMB_2017_051_7

[1] [1] Ahlfors, L. V., Möbius transformations in several dimensions. Ordway Professorship Lectures in Mathematics, University of Minnesota, School of Mathematics, Minneapolis, MN, 1981. Google Scholar

[2] [2] Colonna, F., The Block constant of bounded harmonic mappings. Indiana Univ. Math. J. 38(1989), 829–840. http://dx.doi.Org/10.1512/iumj.1989.38.38039 Google Scholar

[3] [3] Holland, F. and Walsh, D., Criteriafor membership of Block Space and its subspace, BMOA. Math. Ann. 273(1986), 317–335. http://dx.doi.org/10.1007/BF01451410 Google Scholar

[4] [4] Pavlovic, M., On the Holland-Walsh characterization of Block functions. Proc. Edinb. Math. Soc. 51(2008), 439–441. http://dx.doi.org/10.1017/S0013091506001076 Google Scholar

[5] [5] Ren, G. and Tu, C., Block Space in the unit ball of Cn. Proc. Amer. Math. Soc. 133(2005), 719–726. http://dx.doi.org/10.1090/S0002-9939-04-07617-8 Google Scholar

[6] [6] Vuorinen, M., Conformal geometry and quasiregular mappings. Lecture Notes in Mathematics, 1319, Springer-Verlag, Berlin, 1988. http://dx.doi.Org/10.1007/BFb0077904 Google Scholar

[7] [7] Zhu, K., Distances and Banach Spaces of holomorphic functions on complex domains. J. London Math. Soc. 49(1994), 163–182. http://dx.doi.Org/10.1112/jlms/49.1.163 Google Scholar

[8] [8] Zhu, K., Bloch type Spaces of analytic functions. Rocky Mountain J. Math. 23(1993), 1143–1177. http://dx.doi.Org/10.1216/rmjm/1181072549 Google Scholar

Cité par Sources :