Abstract
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).