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Abstract. Generalizing the classical result of Bohr, we show that if an nvariable power series converges in n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the modulii of the terms is less than 1 in the homothetic domain r ·D, where r = 1− n 2/3. This constant is near to the best one for the domain D = {z : |z 1 | + . . . + |zn| < 1}.

Integral Representations for Strictly Pseudoconvex and n-Circular Domains 13. Andreotti-Norguet Formula and its Generalizations 58 14. Bergman Kernel Function, Szeg6 Kernel and Integral Representations with a Holomorphic Kernel over the Shilov Boundary 67 15. Integral Representations for Functions Holomorphic in the Classical Domains

The generalized Teukolsky-type master equation in Vaidya-de Sitter space-time is given. I t is found that the massive Dirac field of spin state p = 1 / 2 differs greatly from the massive Dirac field of spin state p=-1/2 in radiative mechanism. This effect originates from the variance of Dirac vacuum near the event horizon in the nonstatic space-time caused by spin state.

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