BMO Estimates for Multilinear Fractional Integrals (Analysis in Theory and Applications, 2012)
In this paper, the authors prove that the multilinear fractional integral operator $T_{Ω,α}^{A_1,A_2}$ and the relevant maximal operator $M_{Ω,α}^{A_1,A_2}$ with rough kernel are both bounded from $L^p$ $(1 < p < ∞)$ to $L^q$ and from $L^p$ to $L^{n/(n−α),∞}$ with power weight, respectively, where$$T_{Ω,α}^{A_1,A_2}(f)(x) =\int_{R^n}\frac{R_{m_1}(A_1;x,y)R_{m_2}(A_2;x,y)}{|x-y|^{n-α+m_1+m_2-2}}Ω(x-y)f(y)dy$$and$$M_{Ω,α}^{A_1,A_2}(f)(x)= \sup_{r > 0}\frac{1}{r^{n−α+m_1+m_2−2}}\int_{|x−y|