On Lusin's area integrals and g-functions in certain Dunkl and Laguerre settings

We investigate $g$-functions and Lusin's area type integrals related to certain multi-dimensional Dunkl and Laguerre settings. We prove that the considered square functions are bounded on weighted $L^p$, $1<p<\infty$, and from $L^1$ into weak $L^1$.