Fractional integrals and generalized olsen inequalities

Abstract

Let Tρ be the generalized fractional integral operator associated to a function ρ: (0, ∞) → (0, ∞), as defined in [16]. For a function W on R{double-struck}n, we shall be interested in the boundedness of the multiplication operator f {mapping} W Tρf on generalized Morrey spaces. Under some assumptions on ρ, we obtain an inequality for W Tρ, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.