On the extension in the Hardy classes and the Nevanlinna class

Jaakko Hyvönen; Juhani Riihentaus

Bulletin de la Société Mathématique de France (1984)

  • Volume: 112, page 469-480
  • ISSN: 0037-9484

How to cite

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Hyvönen, Jaakko, and Riihentaus, Juhani. "On the extension in the Hardy classes and the Nevanlinna class." Bulletin de la Société Mathématique de France 112 (1984): 469-480. <http://eudml.org/doc/87473>.

@article{Hyvönen1984,
author = {Hyvönen, Jaakko, Riihentaus, Juhani},
journal = {Bulletin de la Société Mathématique de France},
keywords = {extension in Hardy classes; extension in the Nevanlinna class; polar set; harmonic majorant; holomorphic extension; removable singularities for subharmonic functions},
language = {eng},
pages = {469-480},
publisher = {Société mathématique de France},
title = {On the extension in the Hardy classes and the Nevanlinna class},
url = {http://eudml.org/doc/87473},
volume = {112},
year = {1984},
}

TY - JOUR
AU - Hyvönen, Jaakko
AU - Riihentaus, Juhani
TI - On the extension in the Hardy classes and the Nevanlinna class
JO - Bulletin de la Société Mathématique de France
PY - 1984
PB - Société mathématique de France
VL - 112
SP - 469
EP - 480
LA - eng
KW - extension in Hardy classes; extension in the Nevanlinna class; polar set; harmonic majorant; holomorphic extension; removable singularities for subharmonic functions
UR - http://eudml.org/doc/87473
ER -

References

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  1. [1] ABRAHAMSSON (L.). — Meromorphic extension of holomomorphic functions with growth conditions, Bull. Soc. Math. Fr., Vol. 110, 1982, pp. 417-427. Zbl0523.32008MR84i:32019
  2. [2] CEGRELL (U.). — Removable singularity sets for analytic functions having modulus with bounded Laplace mass, Proc. Amer. Math. Soc., Vol. 88, 1983, pp. 283-286. Zbl0514.32011MR84g:32024
  3. [3] CIMA (J.) and GRAHAM (I.). — On the extension of holomorphic functions with growth conditions across analytic subvarieties, Michigan Math. J., Vol. 28, 1981, pp. 241-256. Zbl0438.32008MR82j:32030
  4. [4] FEDERER (H.). — Geometric measure theory, Berlin, Springer, 1969. Zbl0176.00801MR41 #1976
  5. [5] HARVEY (R.) and POLKING (J.). — Extending analytic objects, Comm. Pure Appl. Math., Vol. 28, 1975, pp. 701-727. Zbl0323.32013MR53 #13642
  6. [6] HAYMAN (W.) and KENNEDY (P.). — Subharmonic functions, I, London, Academic Press, 1976. Zbl0419.31001MR57 #665
  7. [7] HEINS (M.). — Hardy classes on Riemann surfaces, Berlin, Springer, 1971. 
  8. [8] HERVÉ (M.). — Analytic and plurisubharmonic functions in finite and infinite dimensional spaces, Berlin, Springer, 1970. 
  9. [9] JÄRVI (P.). — Removable singularities for Hp-functions, Proc. Amer. Math. Soc., Vol. 86, 1982, pp. 596-598. Zbl0532.32004
  10. [10] LELONG (P.). — Ensembles singuliers impropres des fonctions plurisousharmoniques, J. Math. Pures Appl., Vol. 36, 1957, pp. 263-303. Zbl0122.31902MR19,1194a
  11. [11] LELONG (P.). — Plurisubharmonic functions and positive differential forms, New York, Gordon and Breach, 1969. Zbl0195.11604
  12. [12] MATTILA (P.). — An integral inequality for capacities, Math. Scand., Vol. 53, 1983, pp. 256-264. Zbl0513.31006MR85f:31016
  13. [13] PARREAU (M.). — Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. Inst. Fourier, Grenoble, Vol. 3, 1951, pp. 103-197. Zbl0047.32004MR14,263c
  14. [14] RIIHENTAUS (J.). — An extension theorem for meromorphic functions of several variables, Ann. Acad. Sc. Fenn., Sér. A I, Vol. 4, 1978/1979, pp. 145-149. Zbl0421.32017MR80e:32007
  15. [15] RIIHENTAUS (J.). — On the extension of holomorphic functions with growth conditions, J. London Math. Soc., (2), Vol. 27, 1983, pp. 281-288. Zbl0479.30007MR85b:32021
  16. [16] RIIHENTAUS (J.). — On the extension of separately hyperharmonic functions and Hp-functions, Michigan Math J., Vol. 31, 1984, pp. 99-112. Zbl0585.32008MR85j:32023
  17. [17] RONKIN (L.). — Introduction to the theory of entire functions of several variables, Providence: Amer. Math. Soc., 1974. Zbl0286.32004MR49 #10901
  18. [18] RUDIN (W.). — Function theory in the unit ball of Cn, New York, Springer, 1980. Zbl0495.32001MR82i:32002
  19. [19] SADULLAEV (A.). — Rational approximation and pluripolar sets (Russian), Mat. Sbornik, Vol. 119, 1982, pp. 96-118. Zbl0511.32011MR84d:32026
  20. [20] SHIFFMAN (B.). — On the removal of singularities of analytic sets, Michigan Math. J., Vol. 15, 1968, pp. 111-120. Zbl0165.40503MR37 #464
  21. [21] STEIN (E.). — Boundary behavior of holomorphic functions of several complex variables, Princeton, Princeton University Press, 1972. Zbl0242.32005MR57 #12890

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