Geodesic
Generalization of a~theorem of Men'shov on monogenic functions
Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 221-231

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It is shown that in Men'shov's theorem on the holomorphicity of continuous functions monogenic at each point of a domain with respect to two intervals intersecting at this point the condition of continuity of $f(z)$ may be replaced by the condition of summability of $(\log^+|f(z)|)^p$ for all positive $p2$. As a collateral result a theorem of Phragmén–Lindelöf type is proved in which a certain summability condition is imposed in place of a condition on the growth of the function. Bibliography: 17 titles. 
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     title = {Generalization of a~theorem of {Men'shov} on monogenic functions},
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D. S. Telyakovskii. Generalization of a~theorem of Men'shov on monogenic functions. Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 221-231. http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a10/