On boundary properties of the components of polyharmonic functions
Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 821-834.

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The following two classes of functions are introduced for $p\ge0$: the class $CU^p(G)$ of uniformly continuous functions of order $p$ in a domain $G\subset\mathbb C$, and the class $\mathfrak M^p(G)$ of functions of the boundedness of order $p$ in $G$. Criterions are established for an $n$-analytic function to belong to each of these classes.
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E. P. Dolzhenko. On boundary properties of the components of polyharmonic functions. Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 821-834. http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a2/

[1] Balk M. B., Polyanalytic Functions, Math. Res., 63, ed. M. Reissig, Akademie-Verlag, Berlin, 1991 | MR | Zbl

[2] Davis P. J., The Schwarz Function and Its Applications, Carus Math. Monographs, 17, Math. Assoc. America, Washington (D.C.), 1974 | Zbl

[3] Mathurin C., Fonction caracteristique d'un contour algebrique simple. Application a l'equation $\Delta(\Delta\phi)=0$ de l'elastostatique plane, Notes techniques du Ministere de l'Air, 105, Service de Documentation et d'Information technique de l'Aeronautique, Paris, 1962 | Zbl

[4] Dolzhenko E. P., “Ob osobykh tochkakh nepreryvnykh garmonicheskikh funktsii”, Izv. AN SSSR. Ser. matem., 28:6 (1964), 1251–1270 | MR | Zbl

[5] Tamrazov P. M., “Konturnye i telesnye strukturnye svoistva golomorfnykh funktsii kompleksnogo peremennogo”, UMN, 28:1 (1973), 131–161 | MR | Zbl

[6] Barth K. F., Schneider W. J., “On the impossibility for extending the Riesz uniqueness theorem to functions of slow growth”, Ann. Acad. Sci. Fenn. Ser. A. I Math., 432 (1968), 1–9 | MR

[7] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M.–L., 1950

[8] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966

[9] Khop N. T., “O normalnoi razreshimosti zadachi Dirikhle dlya odnoi ellipticheskoi sistemy”, Differents. uravneniya, 2:2 (1966), 214–225 | MR

[10] Rasulov K. M., “O reshenii kraevykh zadach tipa zadachi Dirikhle dlya polianaliticheskikh funktsii”, Dokl. AN SSSR, 309:6 (1989), 1309–1313