  The present paper, we study in the harmonic analysis associated to the
Weinstein operator, the boundedness on Lp of the uncentered maximal function.
First, we establish estimates for the Weinstein translation of characteristic
function of a closed ball with radius " centered at 0 on the upper half space.
Second, we prove weak-type L1-estimates for the uncentered maximal function
associated with the Weinstein operator and we obtain that is bounded on Lp for
p>1.
