Cesàro means of Jacobi expansions on the parabolic biangle

We study Cesàro (C, δ) means for two-variable Jacobi polynomials on the parabolic biangle B = {(x1, x2) ∈ R2 : 0 ≤ x1 ≤ x2 ≤ 1}. Using the product formula derived by Koornwinder & Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C, δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ > α + β + 1, α − 1 2 ≥ β ≥ 0. Furthermore, for δ ≥ α+ 2β + 32 the means define positive linear operators.