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http://dx.doi.org/10.4134/BKMS.2012.49.1.011

INNER UNIFORM DOMAINS, THE QUASIHYPERBOLIC METRIC AND WEAK BLOCH FUNCTIONS  

Kim, Ki-Won (Department of Mathematics Education Silla University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.1, 2012 , pp. 11-24 More about this Journal
Abstract
We characterize the class of inner uniform domains in terms of the quasihyperbolic metric and the quasihyperbolic geodesic. We also characterize uniform domains and inner uniform domains in terms of weak Bloch functions.
Keywords
inner uniform domains; the quasihyperbolic metric and weak Bloch functions;
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1 K. Kim and N. Langmeyer, Harmonic Measure and Hyperbolic distance in John disks, Math. Scand. 83 (1998), no. 2, 283-299.   DOI
2 N. Langmeyer, The quasihyperbolic metric, growth and John domains, University of Michigan Ph.D. Thesis, 1996.
3 N. Langmeyer, The quasihyperbolic metric, growth and John domains, Ann. Acad. Sci. Fenn. Math. 23 (1998), no. 1, 205-224.
4 J. Vaisala, Relatively and inner uniform domains, Conform. Geom. Dyn. 2 (1998), 56-88.   DOI
5 O. J. Broch, Geometry of John disks, Norwegian University of Science and Technology Doctoral Thesis, 2005.
6 Z. Balogh and A. Volberg, Boundary Harnack principle for separated semihyperbolic repellers, harmonic measure applications, Rev. Mat. Iberoamericana 12 (1996), no. 2, 299-336.
7 Z. Balogh and A. Volberg, Geometric localization, uniformly John property and separated semihyperbolic dynamics, Ark. Mat. 34 (1996), no. 1, 21-49.   DOI   ScienceOn
8 M. Bonk, J. Heinonen, and P. Koskela, Uniformizing Gromov hyperbolic spaces, Asteroque 270 (2001), viii+99 pp.
9 F. W. Gehring, K. Hag, and O. Martio, Quasihyperbolic geodesics in John domains, Math. Scand. 65 (1989), no. 1, 75-92.   DOI
10 F. W. Gehring and W. F. Hayman, An inequality in the theory of conformal mapping, J. Math. Pures Appl. (9) 41 (1962), 353-361.
11 F. W. Gehring and B. G. Osgood, Uniform domains and the quasihyperbolic metric, J. Analyse Math. 36 (1979), 50-74.   DOI   ScienceOn
12 F. W. Gehring and B. P. Palka, Quasiconformal homogeneous domains, J. Analyse Math. 30 (1976), 172-199.   DOI   ScienceOn
13 J. Heinonen and S. Rohde, The Gehring and Hayman inequality for quasihyperbolic geodesics, Math. Proc. Cambridge Philos. Soc. 114 (1993), no. 3, 393-405.   DOI
14 K. Kim, The quasihyperbolic metric and analogues of the Hardy-Littlewood property for $\alpha$ = 0 in uniformly John domains, Bull. Korean Math. Soc. 43 (2006), no. 2, 395-410.   DOI   ScienceOn