Abstract. The action of the generalized fractional integral operators and the generalized fractional maximal operators is investigated in the framework of Morrey spaces. A typical property of the functions which belongs to Morrey spaces under pointwise multiplication by the generalized fractional integral operators and the generalized fractional maximal operators is established. The boundedness property of the fractional integral operators on the predual of Morrey spaces is shown as well. A counterexample concerning the FeffermanPhong inequality is given by the use of the characteristic function of the Cantor set.

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We show some inequalities for generalized fractional integral operators on generalized Morrey spaces. We also show the boundedness property of the generalized fractional integral operators on the predual of the generalized Morrey spaces.

Abstract. In this paper, we study boundedness of integral operators on generalized Morrey spaces and its application to estimates in Morrey spaces for the Schrödinger operator L 2 = −∆ + V (x) + W (x) with nonnegative V ∈ (RH)∞ (reverse Hölder class) and small perturbed potentials W .