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We consider the boundedness of fractional integral operators with rough kernel from Morrey spaces Lp,λ to Lq,μ . Our main concern is proving the boundedness property for μ < λ as an extension of Adams inequality on some special subsets of the operator’s domain namely classes of Ap , simple function, and radial function respectively. For radial function, we prove the boundedness on local Morrey spaces. We also prove the boundedness property for μ λ as well as the special case of q p . It is interesting on its own term since the operator is not bounded from Lp to Lq if q p . We also establish necessary conditions for boundedness. Our proposed condition for boundedness includes the sufficient conditions for both Adams inequality and Spanne inequality. Mathematics subject classification (2010): 42B20, 42B25.

Rough fractional integral operators and beyond Adams inequalities