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

Abstract EN

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 .