In this work, we prove Clarkson-type and Nash-type inequalities in the Dunkl setting on [Formula: see text] for [Formula: see text]-functions. By combining these inequalities, we show Heisenberg-type inequalities for the Dunkl transform on [Formula: see text], and we deduce local-type uncertainty inequalities for the Dunkl transform on [Formula: see text].
We prove a version of Heisenberg-type uncertainty principle for the Dunkl-Wigner transform of magnitude s>0; and we deduce a local uncertainty principle for this transform.
Uncertainty Principles for the Dunkl-Wigner Transforms
