On Estimates of Non-Increasing Rearrangement of Generalized Fractional Maximal Function

Abstract

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.