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We discuss the concept of Sobolev space associated to the Laguerre operator $L_{\alpha }=-yd²/dy²-d/dy+y/4+\alpha ²/4y$, y ∈ (0,∞). We show that the natural definition does not agree with the concept of potential space defined via the potentials ${\left(L_{\alpha }\right)}^{-s}$. An appropriate Laguerre-Sobolev space is defined in order to achieve that coincidence. An application is given to the almost everywhere convergence of solutions of the Schrödinger equation. Other Laguerre operators are also considered.