Sufficient conditions of boundedness of L-index and analog of Hayman's Theorem for analytic functions in a ball
DOI:
https://doi.org/10.24193/subbmath.2018.4.06Keywords:
Analytic function, unit ball, bounded L-index in joint variables, max- imum modulus, partial derivative, bounded L-index in direction.Abstract
We generalize some criteria of boundedness of L-index in joint variables for analytic in an unit ball functions. Our propositions give an estimate maximum modulus of the analytic function on a skeleton in polydisc with the larger radii by maximum modulus on a skeleton in the polydisc with the lesser radii. An analog of Hayman’s Theorem for the functions is obtained. Also we established a connection between class of analytic in ball functions of bounded lj -index in every direction 1j, j ∈ {1, . . . , n} and class of analytic in ball of functions of bounded L-index in joint variables, where L(z) = (l1(z), . . . , ln(z)), lj : Bn → R+ is continuous function, 1j = (0, . . . , 0, 1 , 0, . . . , 0) ∈ Rn , z ∈ Cn. j−th place
Mathematics Subject Classification (2010): 32A05, 32A10, 32A30, 32A40, 30H99.
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