Let $R\left(\mathbb{D}\right)$ be the algebra generated in the Sobolev space ${W}^{22}\left(\mathbb{D}\right)$ by the rational functions with poles outside the unit disk $\overline{\mathbb{D}}$. This is called the *Sobolev disk algebra*. In this article, the commutant of the multiplication operator ${M}_{B\left(z\right)}$ on $R\left(\mathbb{D}\right)$ is studied, where $B\left(z\right)$ is an n-Blaschke product. We prove that an operator $A\in \mathcal{L}\left(R\right(\mathbb{D}\left)\right)$ is in $\mathcal{A}\text{'}\left({M}_{B\left(z\right)}\right)$ if and only if $A={\sum}_{i=1}^{n}{M}_{{h}_{i}}{M}_{\Delta \left(z\right)}^{-1}{T}_{i}$, where $\{{h}_{i}{\}}_{i=1}^{n}\subset R(\mathbb{D})$, and ${T}_{i}\in \mathcal{L}\left(R\right(\mathbb{D}\left)\right)$ is given by $\left({T}_{i}g\right)\left(z\right)={\sum}_{j=1}^{n}(-1{)}^{i+j}{\Delta}_{ij}(z\left)g\right({G}_{j-1}\left(z\right))$, $i=1,2,\dots ,n$, ${G}_{0}\left(z\right)\equiv z$.

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