Necessary and sufficient conditions for the boundedness of rough B-fractional integral operators in the Lorentz spaces

In this paper, the necessary and sufficient conditions are found for the boundedness of the rough Bfractional integral operators from the Lorentz spaces Lp,s,γ to Lq,r,γ , 1 < p < q <∞, 1 r s ∞, and from L1,r,γ to Lq,∞,γ ≡WLq,γ , 1 < q <∞, 1 r ∞. As a consequence of this, the same results are given for the fractional B-maximal operator and B-Riesz potential. © 2007 Elsevier Inc. All rights reserved