On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces. (4th August 2016) - He, Sha; Tao, Xiangxing
Abstract : We study some multilinear operators with rough kernels. For the multilinear fractional integral operators T Ω, α A and the multilinear fractional maximal integral operators M Ω, α A, we obtain their boundedness on weighted Morrey spaces with two weights L p, κ ( u, v ) when D γ A ∈ Λ ˙ β     ( | γ | = m - 1 ) or D γ A ∈ B M O     ( | γ | = m - 1 ) . For the multilinear singular integral operators T Ω A and the multilinear maximal singular integral operators M Ω A, we show they are bounded on weighted Morrey spaces with two weights L p, κ ( u, v ) if D γ A ∈ Λ ˙ β     ( | γ | = m - 1 ) and bounded on weighted Morrey spaces with one weight L p, κ ( w ) if D γ A ∈ B M O     ( | γ | = m - 1 ) for m = 1, 2 .