ON THE BOUNDEDNESS OF A GENERALIZED FRACTIONAL-MAXIMAL OPERATOR IN LORENTZ SPACES

In this paper considers a generalized fractional-maximal operator, special case of which is the classical function. Conditions for function Φ, defines function, and weight functions w v, determine weighted Lorentz spaces Λp(v) Λq(w) (1 < p ≤ q ∞) under maximal-fractional operator bounded from one space to another are obtained. For fractional maximal Hardy-Littlewood such results were previously known. When proving main result, we make essential use an estimate nonincreasing rearrangement operator. addition, introduce supremal conditions boundedness in Lebesgue This result also essentially used proof theorem.