Fractional maximal operator in the local Morrey-Lorentz spaces and some applications

In this study, we obtain the necessary and sufficient conditions for the boundedness of the fractional maximal operator M(alpha)in the local Morrey-Lorentz spaces M-p,q; lambda(loc) (R-n). We use sharp rearrangement inequalities while proving our result. We apply this result to the Schrodinger operator -Delta + V on R-n, where the nonnegative potential V belongs to the reverse Holder class B-infinity(R-n). The local Morrey-Lorentz MMp,q; lambda loc (R-n)-> M-q,s; lambda(loc)(Rn) estimates for the Schrodinger type operators V-gamma(-Delta + V)(-beta) and V-gamma del (-Delta + V)(-beta) are obtained.