  In a recent article J. Aldaz proved that the weak L1 bounds for the centered
maximal operator associated to finite radial measures cannot be taken
independently with respect to the dimension. We show that at least for small p
near to 1 the same result holds for the Lp bounds of such measures with
decreasing densities. We also give some concrete examples, that include
Gaussian measure, where better estimates with respect to the general case are
obtained.
