On estimates of non-increasing rearrangement of generalized fractional maximal function

We give a sharp pointwise estimate of the non-increasing rearrangement of the generalized fractional maximal function $(M_\Phi f)(x)$ via an expression involving the non-increasing rearrangement of $f$. It is shown that the obtained estimate is more sharp than the inequality which follows from the estimate for the generalized Riesz potential.