Weakly invertible elements in anisotropic weighted spaces of holomorphic functions in a polydisc

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.