Abstract :
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
Keywords :
Laplace–Bessel differential operator , Fractional B-maximalfunction , O’Neil type inequality , B-fractional integral , B-convolution , Lorentz space
