Geodesic
Existence of boundary values for metaharmonic functions
Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1417-1448 
V. P. Mikhailov. Existence of boundary values for metaharmonic functions. Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1417-1448. http://geodesic.mathdoc.fr/item/SM_1999_190_10_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions for the existence of $L_2$-limits at the boundary of solutions of a metaharmonic equation in a half-space are established. In the case of Laplace's equation these criteria coincide with Riesz's theorem: a harmonic function has an $L_2$-limit at the boundary if and only if it is $L_2$-bounded.

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