THE QUASIHYPERBOLIC METRIC AND ANALOGUES OF THE HARDY-LITTLEWOOD PROPERTY FOR α

Title & Authors
THE QUASIHYPERBOLIC METRIC AND ANALOGUES OF THE HARDY-LITTLEWOOD PROPERTY FOR α
Kim, Ki-Won;

Abstract
We characterize the class of uniformly John domains in terms of the quasihyperbolic metric and from the result we get some analogues of the Hardy-Littlewood property for ${\alpha} Keywords the quasihyperbolic metric;the Hardy-Littlewood property and uniformly John domains; Language English Cited by 1. INNER UNIFORM DOMAINS, THE QUASIHYPERBOLIC METRIC AND WEAK BLOCH FUNCTIONS,; 대한수학회보, 2012. vol.49. 1, pp.11-24 2. INNER UNIFORM DOMAINS AND THE APOLLONIAN INNER METRIC,;; 대한수학회보, 2013. vol.50. 6, pp.1873-1886 1. INNER UNIFORM DOMAINS, THE QUASIHYPERBOLIC METRIC AND WEAK BLOCH FUNCTIONS, Bulletin of the Korean Mathematical Society, 2012, 49, 1, 11 2. INNER UNIFORM DOMAINS AND THE APOLLONIAN INNER METRIC, Bulletin of the Korean Mathematical Society, 2013, 50, 6, 1873 References 1. Z. Balogh and A. Volberg, Boundary Harnack principle for separated semihy- perbolic repellers, harmonic measure applications, Rev. Mat. Iberoamericana 12 (1996), no. 2, 299-336 2. Z. Balogh and A. Volberg, Geometric localization, uniformly John property and separated semihy- perbolic dynamics, Ark. Mat. 34 (1996), no. 1, 21-49 3. F. W. Gehring, K. Hag, and O. Martio, Quasihyperbolic geodesics in John do- mains, Math. Scand. 65 (1989), no. 1, 75-92 4. F. W. Gehring and O. Martio, Quasidisks and the Hardy-Littlewood property, Complex Variables Theory Appl. 2 (1983), no. 1, 67-78 5. F. W. Gehring and O. Martio, Lipschitz classes and quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 203-219 6. F. W. Gehring and B. G. Osgood, Uniform domains and the quasihyperbolic metric, J. Analyse Math. 36 (1979), 50-74 7. F. W. Gehring and B. P. Palka, Quasiconformally homogeneous domains, J. Analyse Math. 30 (1976), 172-199 8. G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. II, Math. Z. 34 (1932), no. 1, 403-439 9. K. Kim, Lipschitz class, growth of derivative and uniformly John domains, East Asian Math. J. 19 (2003), 291-303 10. K. Kim, Hardy-Littlewood property with the inner length metric, Commun. Ko- rean Math. Soc. 19 (2004), no. 1, 53-62 11. K. Kim and N. Langmeyer, Harmonic measure and hyperbolic distance in John disks, Math. Scand. 83 (1998), no. 2, 283-299 12. R. Kaufman and J. -M. Wu, Distances and the Hardy-Littlewood property, Com- plex Variables Theory Appl. 4 (1984), no. 1, 1-5 13. N. Langmeyer, The quasihyperbolic metric, growth, and John domains, Univer- sity of Michigan Ph.D. Thesis (1996) 14. N. Langmeyer, The quasihyperbolic metric, growth, and John domains, Ann. Acad. Sci. Fenn. Math. 23 (1998), no. 1, 205-224 15. V. Lappalainen, Lip$_{h}\$-extension domains, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 56 (1985), 52pp

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