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Maximum modulus in a bidisc of analytic functions of bounded 𝐋 -index and an analogue of Hayman’s theorem

Andriy BanduraNataliia PetrechkoOleh Skaskiv — 2018

Mathematica Bohemica

We generalize some criteria of boundedness of 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).

Non-homogeneous directional equations: Slice solutions belonging to functions of bounded L -index in the unit ball

Andriy BanduraTetyana SaloOleh Skaskiv — 2024

Mathematica Bohemica

For a given direction 𝐛 n { 0 } we study non-homogeneous directional linear higher-order equations whose all coefficients belong to a class of joint continuous functions which are holomorphic on intersection of all directional slices with a unit ball. Conditions are established providing boundedness of L -index in the direction with a positive continuous function L satisfying some behavior conditions in the unit ball. The provided conditions concern every solution belonging to the same class of functions...

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