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We study approximation properties of weighted $\mathrm{L}^2$-orthogonalprojectors onto spaces of polynomials of bounded degree in the Euclidean unitball, where the weight is of the reflection-invariant form $(1-\lVert x\rVert^2)^\alpha \prod_{i=1}^d \lvert x_i \rvert^{\gamma_i}$, $\alpha,\gamma_1, \dots, \gamma_d > -1$. Said properties are measured inDunkl-Sobolev-type norms in which the same weighted $\mathrm{L}^2$ norm is usedto control all the involved differential-difference Dunkl operators, such asthose appearing in the Sturm-Liouville characterization of similarly weighted$\mathrm{L}^2$-orthogonal polynomials, as opposed to the partial derivatives ofSobolev-type norms. The method of proof relies on spaces instead of bases oforthogonal polynomials, which greatly simplifies the exposition.

Orthogonal polynomial projection error in Dunkl-Sobolev norms in the ball