New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutators

Abstract

AbstractIn this paper, we introduce certain classes of multilinear Calderón–Zygmund operators with kernels of Dini’s type. Applying the sharp method and $A_{\vec{p}}^{\infty }(\varphi )$ A p → ∞ ( φ ) functions, we first establish some weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type, including pointwise estimates, strong type, and weak endpoint estimates. Furthermore, similar weighted norm inequalities for commutators with $\mathrm{BMO}_{\theta }(\varphi )$ BMO θ ( φ ) functions are also obtained, but the weak endpoint estimate is of $L({\mathrm{log}}L)$ L ( log L ) type.