Rough bilinear fractional integrals with variable kernels

We study the rough bilinear fractional integral (B) over tilde (Omega,alpha)(f, g)(x) = integral(Rn) f(x + y)g(x - y) Omega(x, y')/vertical bar y vertical bar(n-alpha) dy, where 0 < alpha < n, Omega is homogeneous of degree zero on the y variable and satisfies Omega is an element of L(infinity)(R(n)) x L(s)(S(n-1)) for some s >= 1, and S(n-1) denotes the unit sphere of R(n). By assuming size conditions on Omega, we obtain several boundedness properties of (B) over tilde (Omega,alpha)(f, g): (B) over tilde (Omega,alpha) : L(p1) x L(p2) -> L(p), where 1/p = 1/p1 + 1/p2 - alpha/n. Our result extends a main theorem of Y. Ding and C. Lin [Math. Nachr., 2002, 246-247: 47-52].