Boundedness of multilinear oscillatory singular integrals on Hardy type spaces

摘要

In this paper, the authors discuss a class of multilinear singular integrals and obtain their boundedness from the weighted Hardy space H_ω~1(R~n) to the weighted Lebesgue space L_ω~1(R~n) for ω ∈ A_1(R~n) (the class of Muckenhoupt's weights) and from the weighted Herz-type Hardy space HK_p(ω_1, ω_2; R~n) (or HK_p (ω_1, ω_2; R~n)) to the weighted Herz space K_p (ω_1, ω_2; R~n) (or K_p( ω_1, ω_2; R~n)) for any p ∈ (1, ∞) and ω_1, ω_2 ∈ A_1(R~n).