A higher order Sobolev-type inner product for orthogonal polynomials in several variables

We consider polynomials in several variables orthogonal with respect to a Sobolev-type inner product, obtained from adding a higher order gradient evaluated in a fixed point to a standard inner product. An expression for these polynomials in terms of the orthogonal family associated with the standard inner product is obtained. A particular case using polynomials in the unit ball is analyzed, and some asymptotic results are derived.