Geodesic
On the existence of angular boundary values for polyharmonic functions in the unit ball
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 144-154 
M. Ya. Mazalov. On the existence of angular boundary values for polyharmonic functions in the unit ball. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 144-154. http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a11/
@article{ZNSL_2017_456_a11,
     author = {M. Ya. Mazalov},
     title = {On the existence of angular boundary values for polyharmonic functions in the unit ball},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {144--154},
     year = {2017},
     volume = {456},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a11/}
}
TY  - JOUR
AU  - M. Ya. Mazalov
TI  - On the existence of angular boundary values for polyharmonic functions in the unit ball
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 144
EP  - 154
VL  - 456
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a11/
LA  - ru
ID  - ZNSL_2017_456_a11
ER  - 
%0 Journal Article
%A M. Ya. Mazalov
%T On the existence of angular boundary values for polyharmonic functions in the unit ball
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 144-154
%V 456
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a11/
%G ru
%F ZNSL_2017_456_a11

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We study boundary properties of polyharmonic functions. In particular, a criterion is obtained (in terms of the radial growth of th derivative) for the existence a.e. of angular boundary values for a polyharmonic function bounded in the unit ball.

[1] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 7, Teoriya uprugosti, izd. 4, Nauka, M., 1983

[2] M. B. Balk, “Polianaliticheskie funktsii i ikh obobscheniya”, Itogi nauki i tekhniki. Sovr. prob. matem. Fund. napr., 85, 1991, 187–246 | MR | Zbl

[3] F. D. Gakhov, Kraevye zadachi, izd. 3, Nauka, M., 1977 | MR

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

[5] L. Karleson, Izbrannye problemy teorii isklyuchitelnykh mnozhestv, Mir, M., 1971 | MR

[6] V. A. Petrov, “Analogi teoremy Fatu dlya polianaliticheskikh funktsii”, Izv. AN Arm. SSR. Matematika, 2:4 (1967), 211–217 | MR | Zbl

[7] M. Nicolesco, Les fonctions polyharmoniques, Hermann, Paris, 1936 | Zbl

[8] G. E. Shilov, Matematicheskii analiz. Vtoroi spetsialnyi kurs, Nauka, M., 1965 | MR

[9] K. O. Besov, “O granichnom povedenii komponent poligarmonicheskikh funktsii”, Matem. zametki, 64:4 (1998), 518–530 | DOI | MR | Zbl

[10] E. P. Dolzhenko, “O granichnom povedenii komponent polianaliticheskoi funktsii”, Matem. zametki, 63:6 (1998), 821–834 | DOI | MR | Zbl

[11] A. Borichev, H. Hedenmalm, “Weighted integrability of polyharmonic functions”, Advances in Math., 264 (2014), 464–505 | DOI | MR | Zbl

[12] E. Almansi, “Sull' integrazione dell' equazione $\Delta^n=0$”, Annali di Matematica Ser. 3, 2 (1899), 1–59 | DOI

[13] W. K. Hayman, B. Korenblum, “Representation and uniqueness theorems for polyharmonic functions”, Journal Anal. Math., 60 (1993), 113–133 | DOI | MR | Zbl

[14] M. B. Balk, M. Ya. Mazalov, “On uniqueness conditions for entire polyharmonic functions”, Partial Differential and Integral Equations, Int. Soc. Anal. Appl. Comput., 2, Kluwer, Dordrecht, 1999, 219–232 | MR | Zbl

[15] H. Render, “Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions”, Duke Math. J., 142:2 (2008), 313–352 | DOI | MR | Zbl