한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제19권4호
  • /
  • Pages.423-435
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  • 2012
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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WEAK BLOCH FUNCTIONS, ∅-UNIFORM AND ∅-JOHN DOMAINS

  • Kim, Ki Won (Department of Mathematics Education, Silla University)
  • 투고 : 2012.09.21
  • 심사 : 2012.11.05
  • 발행 : 2012.11.30
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초록

We give some properties of weak Bloch functions and also give some properties of ${\phi}$-uniform domains and ${\phi}$-John domains in terms of moduli of continuity of Bloch functions and weak Bloch functions.

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참고문헌

  1. M. Bonk, J. Heinonen & P. Koskela: Uniformizing Gromov hyperbolic spaces. Asteroque 270 (2001).
  2. O.J. Broch: Geometry of John disks. Norwegian University of Science and Technology Doctoral Thesis, 2005.
  3. F.W. Gehring, K. Hag & O. Martio: Quasihyperbolic geodesics in John domains. Math. Scand. 65 (1989), 75-92.
  4. F.W. Gehring & O. Martio: Lipschitz classes and quasiconformal mappings. Ann. Acad. Sci. Fenn. Math. 10 (1985), 203-219. https://doi.org/10.5186/aasfm.1985.1022
  5. F.W. Gehring & B.G. Osgood: Uniform domains and the quasi-hyperbolic metric. J. Analyse Math. 36 (1979), 50-74. https://doi.org/10.1007/BF02798768
  6. F.W. Gehring & B.P. Palka: Quasiconformal homogeneous domains. J. Analyse Math. 30 (1976), 172-199. https://doi.org/10.1007/BF02786713
  7. D.A. Herron & M. Vuorinen: Positive harmonic functions in uniform and admissible domains. Analysis 8 (1988), 187-206.
  8. K. Kim: Notes on the moduli of continuity of conjugate harmonic functions in domains. The Bulletin of Natural Science, Silla Univ. 16 (2007), 31-34.
  9. K. Kim: Inner uniform domains, the quasihyperbolic metric and weak Bloch functions. Bull. Korean Math. Soc. 49 (2012), no. 1, 11-24. https://doi.org/10.4134/BKMS.2012.49.1.011
  10. N. Langmeyer: The quasihyperbolic metric, growth and John domains. Ann. Acad. Sci. Fenn. Math. 23 (1998), 205-224.
  11. J. Vaisala: Relatively and inner uniform domains. Conformal Geom. Dynam. 2 (1998), 56-88. https://doi.org/10.1090/S1088-4173-98-00022-8