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Central Asian Problems of Modern Science and Education

Abstract

In this work we give a definition of subharmonic function, where α=(αˈ,αˈˈ) and we show that under additional conditions, these functions belongs to the class φ˄β subharmonic functions.

First Page

58

Last Page

72

References

1. Armitage D.M., Gardiner S.J. Conditions for separately subharmonic functions to be subharmonic, Potential Anal.2. 1993. P.225-261

2. Abdullaev B.I., Imomkulov S.A., Sharipov R.A. subharmonic functions. Contemporary Mathematics. Fundamental Directions (Russian). 2020. (preprint)

3. Arsove M.G. On subharmonicity of doubly subharmonic functions// Proc.Amer. Math. Soc. 1966, № 1, p. 622-626.

4. Avanissian V. Cellule d’Harmonicite et Prolongement Analitique Complexe. Travaux en cours, Hermann, – Paris, 1985.

5. Avanissian V. Fonctions plurisousharmoniques et fonctions doublement sousharmoniques// Ann. Sci. Ecol. Norm. Sup. 1961, № 78. P. 101-161.

6. Bedford E., Taylor B.A. A new capacity for plurisubharmonic functions//Acta.Math. 1982. V.149. pp. 1-40.

7. Bers L., John F., Partial differential equations. Interscience publishers, New York – London – Sydney, 1964. p. 351

8. Cegrell U., Sadullaev A. Separately subharmonical functions// Uzbek Math. J. 1993, №1. P. 78-83

9. Hecart J. M. Ouverts d`harmonicite pour les fonctions separement harmoniques// Potential Anal., 2000, v. 13. № 2. P. 115-126

10. Imomkulov S.A. Separately subharmonic functions// Dokl. UzSSR. 1990, 21, p.8-10.

11. Klimek M. Pluripotential theory. Clarendon Press/Oxford Press, 1991.

12. Kolodzej S., Thorbiornson J. Separately harmonic and subharmonic functions// Potential Anal. 1996, 5, p. 463-466.

13. Lelon P. Fonctions plurisousharmoniques et fonctions analytiques de variables reelles// Ann. Inst. Fourier 11, 1961. p.515-562.

14. Raymond J.S. Fonctions separement analytiques.Ann. de l`inst. Fourier, tom 40, № 1, 1990, p. 79-101

15. Riihentaus J. On a theorem of Avanissian-Arsove// Exposition. Math. 1989, 7, p.69-72.

16. Riihentaus J. On separately subharmonic and harmonic functions.//Complex variables and elliptic equations. An international journal. Volume 59, 2014- issue 2. P.149-161.

17. Sachiko Homano. Hartogs – Osgud theorem for separately harmonic functions. Proc. Japan Acad.,vol.83, Ser. A , 2007, p. 19-18.

18. Sadullaev A., Abdullaev B.I., Potential theory in the class of m-subharmonic functions.// Proc. Steklov Inst. Math. 2012, 279, pp. 155–180.

19. Sadullaev A.C. On separately subharmonic functions (Lelong`s problem). Ann. Fac. Sci. Toulouse. Math., 2011, v. XX, №2, p.183-187.

20. Sadullaev A.S., Imomkulov S.A., Extension of holomorphic and pluriharmonic functions with subtle singularities on parallel sections, Proceedings of the MIRAN named after V.A. Steklov, 253(2006), 158-174

21. Sadullaev A.S., Plurisubharmonic measures and capacities on complex manifolds, UMN, 36(4) (1981), 53-105.

22. Sadullaev A.S., Plurisubharmonic functions, Results of Science and Technology. Modern problems of mathematics. Fundamental directions. Moscow. VINITI, 8(1985), 65-111.

23. Sičiak J. Separately analytic functions and envelopes of holomorphy of some lowerdimensional subsets of // Ann. Pol. Math. – 1969.– V. 22, №1. – P. 145-171.

24. Sičiak J. Singular sets of separately analytic functions. Proceedings of the international workshop, Wuppertal, Aspects of mathematics. ASMA, v.1. 1990.

25. Vaisova M.D. Potential theory in the class of -subharmonic functions (Russian)// Uzbek Mathematical Journal, – Tashkent, 2016, 3, pp. 46–52.

26. Wiegerinck J. Separately subharmonic functions need not be subharmonic// Proc.Amer. Math. Soc. 1988, № 104. P.770-771.

27. Zakharyuta V.P., Separate-analytic functions, generalized Hartogs theorems and hulls of holomorphy, Math. Coll., 101(1976), №1, 57-76.

28. Zbigniev Blocki. Singular sets of separately analytic functions. Ann.Polon.Math. LVI. 2, 1992. P.219-225

29. Zeriahi A. Bases communes dans certains espaces de fonctions harmoniques et fonctions separement harmoniques sur certains ensembles de // Ann. Fac. Sci. Toulouse. Math., 1982, ser. 5. V.4. p.75-102.

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