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Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

It is known that, the m−subharmonic measure of a set E ⊂ D,  related to a domain D ⊂ ℂn, is defined by m−subharmonic functions in D. In this article we define a generalization of the m−subharmonic measures and prove some of their properties.

First Page

76

Last Page

86

References

1. Sadullaev A., Abdullaev B. Potential theory in the class of m-subharmonic functions. Trudy Mat. Inst. Steklova, 279, pp. 166-192 (2012). (in Russian)

2. Sadullaev A. Pluripotential theory. Applications. Palmarium Academic Publishing, 307 p. (2012). (in Russian)

3. Sadullaev A. Plurisubharmonic functions. Sovrem. Probl. Mat. Fund. Naprav. VINITI, Vol. 8, pp. 65-113 (1985). (in Russian)

4. Sadullaev A. Plurisubharmonic measures and capacities on complex manifolds. Uspekhi Mat. Nauk. Vol. 36, Issue 4, pp. 53-105 (1981). (in Russian)

5. Blocki Z. Weak solutions to the complex Hessian equation. Ann. Inst. Fourier, Grenoble. Vol. 5, No. 55, pp. 1735-1756 (2005). (in French)

6. Bedford E., Taylor B.A. A new capacity for plurisubharmonic functions. Acts Math. Vol. 149, No. 1-2, pp. 1-40 (1982).

7. Siciak J. Extremal plurisubharmonic functions in ℂn. Annales Polonici Mathematici. Vol. 1, No. 39, pp. 175-211 (1981).

8. Zaharjuta V.P. Extremal plurisubharmonic functions, Hilbert scales, and the isomorphism of spaces of analytic functions of several variables. I, II. Theory of functions, functional analysis and their applications. T. 19, pp. 133-157, T. 21, p. 65-83 (1974). (in Russian)

9. Brelot M. The Basis of the Classical Potential Theory. Mir, Moscow (1964). (in Russian)

10. Narzillaev N.Kh. About ψ−regular points. Tashkent, Acta NUUz, No. 2.2, pp. 173-175 (2017). (in Russian)

11. Alan M.A. Weighted regularity and two problems of Sadullaev on weighted regularity. Complex Analysis and its Synergies, Springer. Vol. 5, pp. 1-7 (2019).

12. Bloom T., Levenberg N. Weighted pluripotential theory in ℂn. American Journal of Mathematics. Vol. 125:1, pp. 57-103 (2003).

13. Whitney H. Analytic extensions of differentiable functions defined in closed sets. Trans. American Mathematical Society, pp. 63-89 (1934).

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