On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces

Abstract

We study some multilinear operators with rough kernels. For the multilinear fractional integral operators TΩ,αA and the multilinear fractional maximal integral operators MΩ,αA, we obtain their boundedness on weighted Morrey spaces with two weights Lp,κ(u,v) when DγA∈Λ˙β (|γ|=m-1) or DγA∈BMO (|γ|=m-1). For the multilinear singular integral operators TΩA and the multilinear maximal singular integral operators MΩA, we show they are bounded on weighted Morrey spaces with two weights Lp,κ(u,v) if DγA∈Λ˙β (|γ|=m-1) and bounded on weighted Morrey spaces with one weight Lp,κ(w) if DγA∈BMO (|γ|=m-1) for m=1,2.