Korous type inequalities for orthogonal polynomials in two variables

Abstract

Important result for general orthogonal polynomials in one variable reached J. Korous. He dealt with the boundedness and uniform boundedness of polynomials  orthonormal with the weight function

where  is the weight function of another system of polynomials  orthonormal in the same interval and

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