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Keywords:
analytic function; bidisc; bounded ${\mathbf L}$-index in joint variables; maximum modulus; partial derivative; Cauchy's integral formula
analytic function; bidisc; bounded ${\mathbf L}$-index in joint variables; maximum modulus; partial derivative; Cauchy's integral formula
Summary:
We generalize some criteria of boundedness of $\mathbf {L}$-index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p+1)$th partial derivative by lower order partial derivatives (analogue of Hayman's theorem).
References:
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