By using the symmetry of Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and logarithmic Sobolev for transform. Combining these inequalities, obtain new, short proof Heisenberg-type uncertainty principles in setting. Moreover, by combining Nash’s inequality, Carlson’s Sobolev’s embedding theorems transform, new inequalities involving L∞-norm. Finally, Lp-spaces, from which de...

Abstract Recently, deformed quantum systems have received lots of attention in the literature. Dunkl formalism differs from others by containing difference-differential and reflection operator. It is one most interesting deformations since it let us discuss solutions according to even odd solutions. In this work, we studied ideal Bose gas blackbody radiation via formalism. To end, made a liaiso...

In this paper, we show the inclusion and the density of the Schwartz space in Besov–Dunkl spaces and we prove an interpolation formula for these spaces by the real method. We give another characterization for these spaces by convolution. Finally, we establish further results concerning integrability of the Dunkl transform of function in a suitable Besov–Dunkl space.