  In this paper, we will give some results on the support of Dunkl translations
on compactly supported functions. Then we will define Dunkl-type $BMO$ space
and Riesz transforms for Dunkl transform on $L^\infty$, and prove the
boundedness of Riesz transforms from $L^\infty$ to Dunkl-type $BMO$ space under
the uniform boundedness assumption of Dunkl translations. The proof and the
definition in Dunkl setting will be harder than in the classical case for the
lack of some similar properties of Dunkl translations to that of classical
translations. We will also extend the preciseness of the description of support
of Dunkl translations on characteristic functions by Gallardo and Rejeb to that
on all nonnegative radial functions in $L^2(m_k)$.
