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Our main goal in this article is to study mixed norm estimates for theCes\`{a}ro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$.These expansions arise when one consider the Dunkl--Hermite operator (or Dunklharmonic oscillator) $H_{\kappa}:=-\Delta_{\kappa}+|x|^2$, where$\Delta_{\kappa}$ stands for the Dunkl--Laplacian. It is shown that the desiredmixed norm estimates are equivalent to vector-valued inequalities for asequence of Ces\`{a}ro means for Laguerre expansions with shifted parameter. Inorder to obtain the latter, we develop an argument to extend these operatorsfor complex values of the parameters involved and apply a version of threelines lemma.

Mixed norm estimates for the Ces\`aro means associated with Dunkl--Hermite expansions