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Harmonic functions of bounded mean oscillation and a generalization to vector lattices of continuous functions

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Potential Theory Copenhagen 1979

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 787))

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References

  1. M. Arsove and H. Leutwiler, Infinitesimal generators and quasi-units in potential theory, Proc.Nat. Acad. Sci. USA, Vol. 72, No 7, (1975), 2498–2500.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Arsove and H.Leutwiler, A unified theory of harmonic measures and capacitary potentials, to appear.

    Google Scholar 

  3. A. Baernstein II, Univalence and bounded mean oscillation, Michigan Math. J. 23 (1976), 217–223.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Bauer, Silovscher Rand und Dirichletsches Problem, Ann. Inst. Fourier 11 (1961), 86–136.

    Article  MathSciNet  MATH  Google Scholar 

  5. H.S. Bear, Lectures on Gleason parts, Lecture Notes in Math. no. 121, Springer, 1970

    Google Scholar 

  6. M. Brelot, Axiomatique des fonctions harmonique, Université de Montréal, 1966.

    Google Scholar 

  7. J.A. Cima and G. Schober, Analytic functions with bounded mean oscillation and logarithms of Hp functions, Math.Z. 151 (1976) 295–300.

    Article  MathSciNet  MATH  Google Scholar 

  8. C.Constantinescu and A.Cornea, Potential theory on harmonic spaces, Springer-Verlag 1972.

    Google Scholar 

  9. P.L.Duren, Theory of Hp spaces, New York, 1970

    Google Scholar 

  10. C. Fefferman and E.M. Stein, Hp spaces of several variables, Acta Math. 129 (1972), 137–193.

    Article  MathSciNet  MATH  Google Scholar 

  11. W.K. Hayman and C. Pommerenke, On analytic functions of bounded mean oscillation, Bull.London Math. Soc., 10 (1978), 219–224.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Heins, On the principle of harmonic measure, Comment. Math. Helv. 33 (1959), 47–58.

    Article  MathSciNet  MATH  Google Scholar 

  13. F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl.Math. 14 (1961), 415–426

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Leutwiler, Harmonic functions of bounded mean oscillation, to appear in Mathematische Annalen.

    Google Scholar 

  15. T.Lyons, A definition of BMOp for an abstract harmonic space and a John-Nirenberg theorem, to appear in Bull. London Math.Soc.

    Google Scholar 

  16. C. Pommerenke, Schlichte Funktionen und analytische Funktionen beschränkter mittlerer Oszillation, Comment. Math. Helv. 52 (1977) 591–602

    Article  MathSciNet  MATH  Google Scholar 

  17. H.M.Reimann and T.Rychener, Funktionen beschränkter mittlerer Oszillation, Lecture Note in Math. no. 487, Springer, 1975

    Google Scholar 

  18. G. Schober, A geometric condition for bounded mean oscillation, Math.Z.161 (1978), 291–292.

    Article  MathSciNet  MATH  Google Scholar 

  19. J.C. Taylor, The Feller and Silov boundaries of a vector lattice, Illinois J. of Math. 10 (1966), 680–693.

    MathSciNet  MATH  Google Scholar 

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Christian Berg Gunnar Forst Bent Fuglede

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© 1980 Springer-Verlag

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Leutwiler, H. (1980). Harmonic functions of bounded mean oscillation and a generalization to vector lattices of continuous functions. In: Berg, C., Forst, G., Fuglede, B. (eds) Potential Theory Copenhagen 1979. Lecture Notes in Mathematics, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086335

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  • DOI: https://doi.org/10.1007/BFb0086335

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  • Print ISBN: 978-3-540-09967-3

  • Online ISBN: 978-3-540-39183-8

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