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Fine and admissible convergence for the unit ball in ℂn

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Potential Theory Copenhagen 1979

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

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Bibliography

  1. Brelot, M. and Doob, J.L., Limites angulaires et limites fines, Ann. Inst. Fourier 13 (2) (1963), 395–415.

    Article  MathSciNet  MATH  Google Scholar 

  2. Debiard, A., Espaces H p géométriques et probabilistes sur l'espace hermitien hyperbolique D den, n>1. C.R. Acad. Sci. Paris Sér. A–B 281 (1975) no. 23, Aii, A1023–A1026.

    MathSciNet  Google Scholar 

  3. Furstenberg, H., A Poisson formula for semi-simple Lie groups, Annals of Math. 77 (1963), 335–386.

    Article  MathSciNet  MATH  Google Scholar 

  4. Koranyi, A., Harmonic functions on hermitian hyperbolic space, Trans. Amer. Math. Soc. 135 (1969), 507–516.

    Article  MathSciNet  MATH  Google Scholar 

  5. Koranyi, A., A survey of harmonic functions on symmetric spaces, to appear in Proceedings of Symposia in Pure Mathematics, Harmonic Analysis in Euclidean Spaces, American Mathematical Society.

    Google Scholar 

  6. Koranyi, A. and Putz, R.B., Local Fatou theorem and area theorem for symmetric spaces of rank one, Trans. Amer. Math. Soc. 224 (1976), 157–168.

    Article  MathSciNet  MATH  Google Scholar 

  7. Koranyi, A. and Taylor, J.C., Fine and admissible convergence for symmetric spaces of rank one, to appear.

    Google Scholar 

  8. Linden, O., Fatou theorems for the eigenfunctions of the Laplace-Beltrami operator, Thesis, Yeshiva University 1977.

    Google Scholar 

  9. Malliavin, P., Fonctions de Green d'un ouvert strictement pseudoconvexe et classe de Nevanlinna, C.R. Acad. Sci. Paris Sér. A 278 (1974), 141–144.

    MathSciNet  MATH  Google Scholar 

  10. Marcinkiewicz J. and Zygmund, A., On the summability of double Fourier series, Fund. Math. 32 (1969), 122–132.

    MATH  Google Scholar 

  11. Michelson, H.L., Fatou theorems for eigenfunctions of the invariant differential operators on symmetric spaces, Trans. Amer. Math. Soc. 177 (1973), 257–274.

    Article  MathSciNet  MATH  Google Scholar 

  12. Serrin, J., On the Harnack inequality for linear elliptic equations, Journal d'Analyse Math. 4 (1955/56), 292–308.

    Article  MathSciNet  MATH  Google Scholar 

  13. Stein, E.M., Boundary behaviour of holomorphic functions of several complex variables, Princeton University Press, Princeton, N.J. 1972.

    MATH  Google Scholar 

  14. Stein, E.M., Maximal functions: Poisson integrals on symmetric spaces, Proc. Nat. Acad. Sci. USA 73 (1976), 2547–2549.

    Article  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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Taylor, J.C. (1980). Fine and admissible convergence for the unit ball in ℂn . 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/BFb0086342

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  • DOI: https://doi.org/10.1007/BFb0086342

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09967-3

  • Online ISBN: 978-3-540-39183-8

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