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Analytic functions in the unit ball of bounded L-index in joint variables and of bounded L-index in direction: a connection between these classes

Bandura Andriy, Skaskiv Oleh

Demonstratio Mathematica

2019

Vol. 52, nr 1

82--87

We give negative answer to the question of Bordulyak and Sheremeta for more general classes of entire functions than in the original formulation: Does index boundedness in joint variables for an entire function F imply index boundedness in the variable zj for the function F? This question is addressed for entire functions of bounded L-index in joint variables and entire functions of bounded L-index in direction. We also present a class of analytic functions in the unit ball which has bounded L-index in joint variablesand has unbounded l-index in the variables z1 and z2 for any positive continuous function l : B2→C.