Rough bilinear fractional integrals with variable kernels

Abstract

We study the rough bilinear fractional integral where 0<α<n, Ω is homogeneous of degree zero on the y variable and satisfies for some s≥1, and S^n−1 denotes the unit sphere of ℝn. By assuming size conditions on Ω, we obtain several boundedness properties of : where Our result extends a main theorem of Y. Ding and C. Lin [Math. Nachr., 2002, 246―247: 47―52].

Keywords

Bilinear operator / multilinear fractional integral / variable kernel