Beurling-type invariant subspaces of the Poletsky–Stessin–Hardy spaces in the bidisc

The invariant subspaces of the Hardy space $$H^2(\mathbb {D})$$ unit disc are very well known; however, in several variables, structure classical spaces is not yet fully understood. In this study, we examine Poletsky–Stessin–Hardy which generalization to hyperconvex domains $$\mathbb {C}^n$$ . We showed that all $$H^{2}_{\tilde{u}}(\mathbb {D}^2)$$ Beurling-type. To characterize Beurling-type space, first generalized Lax–Halmos Theorem vector-valued and then gave a necessary sufficient condition for be