Dunkl Translation and Uncentered Maximal Operator on the Real Line - Chokri Abdelkefi; Mohamed Sifi (International Journal of Mathematics and Mathematical Sciences)
We establish estimates of the Dunkl translation of the characteristic function χ[−ɛ,ɛ], ɛ>0, and we prove that the uncentered maximal operator associated with the Dunkl operator is of weak type (1,1). As a consequence, we obtain the Lp-boundedness of this operator for 1<p≤+∞.