Boundedness of multilinear oscillatory singular integrals on Hardy type spaces. (English) Zbl 0968.42010
Summary: The authors discuss a class of multilinear singular integrals and obtain their boundedness from the weighted Hardy spaces \(H^1_\omega(\mathbb{R}^n)\) to the weighted Lebesgue space \(L^1_\omega(\mathbb{R}^n)\) for \(\omega\in A_1(\mathbb{R}^n)\) (the class of Muckenhoupt’s weights) and from the weighted Herz-type Hardy space \(H\dot K_p(\omega_1,\omega_2; \mathbb{R}^n)\) (or \(HK_p(\omega_1,\omega_2; \mathbb{R}^n)\)) to the weighted Herz space \(\dot K_p(\omega_1, \omega_2; \mathbb{R}^n)\) (or \(K_p(\omega_1, \omega_2; \mathbb{R}^n)\)) for any \(p\in (1,\infty)\) and \(\omega_1,\omega_2\in A_1(\mathbb{R}^n)\).
MSC:
42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
42B30 | \(H^p\)-spaces |
47A30 | Norms (inequalities, more than one norm, etc.) of linear operators |
47B38 | Linear operators on function spaces (general) |