Geodesic
On regularity theorems for linearly invariant families of harmonic functions
Problemy analiza, Tome 4 (2015) no. 1, pp. 38-56.

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The classical theorem of growth regularity in the class $S$ of analytic and univalent in the unit disc $\Delta$ functions $f$ describes the growth character of different functionals of $f\in S$ and $z\in \Delta$ as $z$ tends to $\partial\Delta.$ Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sense-preserving in $\Delta$ functions which generalized the classical result for the class $S.$ In the presented paper we establish new properties of harmonic sense-preserving functions, connected with the regularity theorems. The effects both common for analytic and harmonic case and specific for harmonic functions are displayed.
Keywords: regularity theorem, linearly invariant family, harmonic function. 
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E. G. Ganenkova; V. V. Starkov. On regularity theorems for linearly invariant families of harmonic functions. Problemy analiza, Tome 4 (2015) no. 1, pp. 38-56. http://geodesic.mathdoc.fr/item/PA_2015_4_1_a2/

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