We introduce the generalized fractional integrals (generalized B-fractional integrals) generated by the ΔB Laplace-Bessel differential operator and give some results for them. We obtain O’Neil type inequalities for the B-convolutions and give pointwise rearrangement estimates of the generalized B-fractional integrals. Then we get the Lp,γ-boundedness of the generalized B-convolution operator, the generalized B-Riesz potential and the generalized fractional B-maximal function. Finally, we prove a sharp pointwise estimate of the nonincreasing rearrangement of the generalized fractional
, and study the modified B-Riesz potential Ĩα, β generated by the generalized shift operator acting in the B-Morrey space in the limiting case.
We prove that the operator Ĩα, β, 0 < α < n + |γ|, is bounded from the B-Morrey space L(n+|γ|−λ)/α,λ,γ(ℝk,+n) to the B-BMO space BMOγ(ℝk,+n).