Landau-Kolmogorov type inequalities in several variables for the Jacobi measure

Abstract

This paper is devoted to Landau-Kolmogorov type inequalities in several variables in L2 norm for Jacobi measures. These measures are chosen in such a way that the partial derivatives of the Jacobi orthogonal polynomials are also orthogonal. These orthogonal polynomials in several variables are built by tensor product of the orthogonal polynomials in one variable. These inequalities are obtained by using a variational method and they involve the square norms of a polynomial p and at most those of the partial derivatives of order 2 of p.

Keywords

• markov-bernstein inequalities
• landau-kolmogorov type inequalities
• l2 norm
• jacobi measure
• orthogonal polynomials
• several variables
• variational method
• sobolev spaces