Korous Type Inequalities for Orthogonal Polynomials in two Variables

J. Korous reached an important result for general orthogonal polynomials in one variable. He dealt with the boundedness and uniform boundedness of polynomials { Pn(x)}^∞_n=0 orthonormal with the weight function

h(x) = δ(x) ̃h(x),

where ̃h(x) is the weight function of another system of polynomials { ̃Pn(x) }^∞_n=0 orthonormal in the same interval and

δ(x) ≥ δ0 > 0

is a certain function. We generalize this result for orthogonal polynomials in two variables multiplying their weight function h(x, y) by a polynomial, dividing h(x, y) by a polynomial, and multiplying h(x, y) with separated variables by a certain function δ(x, y).