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Local behavior of slice holomorphic functions in the unit ball and boundedness of L-index in direction

2022
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AIP Conference Proceedings
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Let b ∈ C n \{0} be a fixed direction and L : B n → R + be a positive continuous function such that L(z) > β|b| 1−|z| , where β > 1 is some constant. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice {z 0 +tb : t ∈ C} with the unit ball For functions from this class we prove some criteria of boundedness of L-index in the direction describing local behavior of maximum modulus, minimum

doi:10.1063/5.0114852
fatcat:kftshyp6iva5tcsx75y6xomo64