Abstract. We consider the boudedness of fractional integral operators on localized (central) Morrey spaces and investigate the relation between the Adams inequality and the Spanne inequality.Mathematics subject classification (2010): 42B20, 42B25.
Shi and Tao [6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein [3] on product of weighted L p -spaces, and got some results. We give some remarks with respect to their results and correct some mistakes. We also consider another multilinear fractional integral introduced by Grafakos [2] .
The boundedness of the various operators onB˙σ-Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization ofB˙σ-Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization ofB˙σ-Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators onB˙σ-Lipschitz spaces is discussed.
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