Some estimates of multilinear operators on tent spaces

Let $0<\alpha <mn$ and $0<r,q<\mathrm{\infty }$. In this paper, we obtain the boundedness of some multilinear operators by establishing pointwise inequalities and applying extrapolation methods on tent spaces $T_r^q({\mathbb{R}}_{+}^{n+1})$, where these multilinear operators include multilinear Hardy–Littlewood maximal operator $\mathcal{M}$, multilinear fractional maximal operator ${\mathcal{M}}_{\alpha }$, multilinear Calderón–Zygmund operator $\mathcal{T}$, and multilinear fractional integral operator ${\mathcal{I}}_{\alpha }$. Therefore, the results of Auscher and Prisuelos–Arribas [Math. Z. 286 (2017), 1575–1604] are extended to the general case.