Geodesic
Weakly invertible elements in anisotropic weighted spaces
Sbornik. Mathematics, Tome 193 (2002) no. 6, pp. 925-943 
F. A. Shamoyan. Weakly invertible elements in anisotropic weighted spaces. Sbornik. Mathematics, Tome 193 (2002) no. 6, pp. 925-943. http://geodesic.mathdoc.fr/item/SM_2002_193_6_a7/
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     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_6_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The question of weak invertibility is studied in weighted $L^p$-spaces of holomorphic functions in a polydisc. A complete description of weight functions such that each non-vanishing bounded holomorphic function in a polydisc is weakly invertible in the corresponding spaces is obtained. In addition, it is shown for $n\geqslant 2$ that, by contrast with the one-dimensional case, the weak invertibility of outer functions is equivalent in a certain sense to the weak invertibility of inner functions.

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