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We study the relation between certain non-degenerate lower Hessenberginfinite matrices $\mathcal{G}$ and the existence of sequences of orthogonalpolynomials with respect to Sobolev inner products. In other words, we extendthe well-known Favard theorem for Sobolev orthogonality. We characterize thestructure of the matrix $\mathcal{G}$ and the associated matrix of formalmoments $\mathcal{M}_{\mathcal{G}}$ in terms of certain matrix operators.

Hessenberg-Sobolev Matrices and Favard type theorems