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In this paper, we present necessary and sufficient conditions of boundedness of  L -index in joint variables for vector-valued functions analytic in the unit ballB   2=    {  z    ∈C   2   :   |   z   |=|    z  1|   2   +   |    z  2|   2&lt;    1  }  ,$\begin{array}{} \mathbb{B}^2\! = \!\{z\!\in\!\mathbb{C}^2: |z|\! = \!\small\sqrt{|z_1|^2+|z_2|^2}\! \lt \! 1\}, \end{array} $    where  L  = ( l  1 ,  l  2 ):  2  →R   +  2$\begin{array}{} \mathbb{R}^2_+ \end{array} $    is a positive continuous vector-valued function.

mathematica slovaca

Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables