| Title:
|
Le minimum de deux fonctions plurisousharmoniques et une nouvelle caracterisation des fonctions holomorphes (French) |
| Title:
|
The minimum of two plurisubharmonic functions and a new characterization of holomorphic functions (English) |
| Author:
|
Abidi, Jamel |
| Author:
|
Ben Yattou, Mohamed Lassaad |
| Language:
|
French |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
301-310 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove, among other results, that $\min (u,v)$ is plurisubharmonic (psh) when $u,v$ belong to a family of functions in ${\rm psh}(D)\cap \Lambda _{\alpha }(D),$ where $\Lambda _{\alpha }(D)$ is the $\alpha $-Lipchitz functional space with $1<\alpha <2.$ Then we establish a new characterization of holomorphic functions defined on open sets of $\mathbb {C}^n.$ (English) |
| Keyword:
|
maximum principle |
| Keyword:
|
plurisubharmonic function |
| MSC:
|
32A10 |
| MSC:
|
32D20 |
| MSC:
|
32U05 |
| MSC:
|
32U30 |
| idZBL:
|
Zbl 1249.32003 |
| idMR:
|
MR2893978 |
| DOI:
|
10.21136/MB.2011.141651 |
| . |
| Date available:
|
2011-09-22T15:00:20Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141651 |
| . |
| Reference:
|
[1] Abidi, J.: Sur le prolongement des fonctions harmoniques.Manuscripta Math. 105 (2001), 471-482. Zbl 1013.31002, MR 1858498, 10.1007/s002290100182 |
| Reference:
|
[2] Abidi, J.: Analycité, principe du maximum et fonctions plurisousharmoniques (à paraitre).. |
| Reference:
|
[3] Carleson, L.: Selected Problems on Exceptional Sets.Van Nostrand, Princeton, N.J., 1967. (Reprint: Wadswarth, Belmont, Cal., 1983). Zbl 0505.00034, MR 0225986 |
| Reference:
|
[4] Cegrell, U.: Removable singularities for plurisubharmonic functions and related problems.Proc. Lond. Math. Soc. 36 (1978), 310-336. Zbl 0375.32013, MR 0484969, 10.1112/plms/s3-36.2.310 |
| Reference:
|
[5] Cegrell, U.: Removable singularity sets for analytic functions having modulus with bounded Laplace mass.Proc. Amer. Math. Soc. 88 (1983), 283-286. Zbl 0514.32011, MR 0695259, 10.1090/S0002-9939-1983-0695259-X |
| Reference:
|
[6] Conway, J. B.: Functions of One Complex Variable II.Springer, Berlin (1995). Zbl 0887.30003, MR 1344449 |
| Reference:
|
[7] Federer, H.: Geometric Measure Theory.Springer, Berlin (1969). Zbl 0176.00801, MR 0257325 |
| Reference:
|
[8] Gunning, R. C., Rossi, H.: Analytic Functions of Several Complex Variables.Prentice-Hall, Englewood Cliffs (1965). Zbl 0141.08601, MR 0180696 |
| Reference:
|
[9] Harvey, R.: Removable singularities for positive currents.Amer. J. Math. 96 (1974), 67-78. Zbl 0293.32015, MR 0361156, 10.2307/2373581 |
| Reference:
|
[10] Harvey, R., Polking, J.: Extending analytic objects.Comm. Pure Appl. Math. 28 (1975), 701-727. MR 0409890, 10.1002/cpa.3160280603 |
| Reference:
|
[11] Hayman, W. K., Kennedy, P. B.: Subharmonic Functions.Academic Press (1976). Zbl 0323.32013 |
| Reference:
|
[12] Henkin, G. M., Leiterer, J.: Theory of Functions on Complex Manifolds.Birkhäuser, Boston, Mass. (1984). Zbl 0726.32001, MR 0774049 |
| Reference:
|
[13] Hervé, M.: Les fonctions analytiques.Presses Universitaires de France (1982). MR 0696576 |
| Reference:
|
[14] Hörmander, L.: An Introduction to Complex Analysis in Several Variables.Van Nostrand, Princeton, N.J. (1966). MR 0203075 |
| Reference:
|
[15] Hyvönen, J., Rühentaus, J.: On the extension in the Hardy classes and in the Nevanlinna class.Bull. Soc. Math. France 112 (1984), 469-480. MR 0802536, 10.24033/bsmf.2017 |
| Reference:
|
[16] Klimek, M.: Pluripotential Theory.Clarendon Press, Oxford (1991). Zbl 0742.31001, MR 1150978 |
| Reference:
|
[17] Krantz, S. G.: Function Theory of Several Complex Variables.Wiley, New York (1982). Zbl 0471.32008, MR 0635928 |
| Reference:
|
[18] Krantz, S. G.: Lipschitz spaces, smoothness of functions, and approximation theory.Expo. Math. 3 (1983), 193-260. Zbl 0518.46018, MR 0782608 |
| Reference:
|
[19] Lelong, P.: Fonctions plurisousharmoniques et formes différentielles positives.Gordon and Breach, New York (1969). MR 0243112 |
| Reference:
|
[20] O'Farrell, A. G.: The 1-reduction for removable singularities, and the negative Hölder spaces.Pro. R. Ir. Acad. A 88 (1988), 133-151. Zbl 0651.46041, MR 0986220 |
| Reference:
|
[21] Poletsky, E.: The minimum principle.Indiana Univ. Math. J. 51 (2003), 269-304. MR 1909290 |
| Reference:
|
[22] Range, R. M.: Holomorphic Functions and Integral Representations in Several Complex Variables.Springer, Berlin (1986). Zbl 0591.32002, MR 0847923 |
| Reference:
|
[23] Ransford, T.: Potential Theory in the Complex Plane.Cambridge University Press (1995). Zbl 0828.31001, MR 1334766 |
| Reference:
|
[24] Riihentaus, J.: On the extension of separately hyperharmonic functions and $H^{p}$-functions.Michigan Math. J. 31 (1984), 99-112. MR 0736475, 10.1307/mmj/1029002968 |
| Reference:
|
[25] Ronkin, L. I.: Introduction to the theory of entire functions of several variables.Amer. Math. Soc., Providence, RI (1974). Zbl 0286.32004, MR 0346175 |
| Reference:
|
[26] Rudin, W.: Function Theory in Polydiscs.Benjamin, New York (1969). Zbl 0177.34101, MR 0255841 |
| Reference:
|
[27] Rudin, W.: Function Theory in the Unit Ball of $\mathbb{C}^n$.Springer, New York (1980). MR 0601594 |
| Reference:
|
[28] Shiffman, B.: On the removal of singularities of analytic sets.Michigan Math. J. 15 (1968), 111-120. Zbl 0165.40503, MR 0224865, 10.1307/mmj/1028999912 |
| Reference:
|
[29] Ullrich, D. C.: Removable sets for harmonic functions.Michigan Math. J. 38 (1991), 467-473. Zbl 0751.31001, MR 1116502, 10.1307/mmj/1029004395 |
| Reference:
|
[30] Verdera, J.: Approximation by solutions of elliptic equations, and Calderon-Zygmund operators.Duke Math. J. 55 (1987), 157-187. Zbl 0654.35007, MR 0883668, 10.1215/S0012-7094-87-05509-8 |
| Reference:
|
[31] Vladimirov, V. S.: Les fonctions de plusieurs variables complexe (et leur application à la théorie quantique des champs).Dunod, Paris (1967). MR 0218608 |
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