Some estimates of multilinear operators on tent spaces

Abstract

Let $ 0 < \alpha < mn $ and $ 0 < r, q < \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.

Keywords

• multilinear maximal operator
• multilinear calderón–zygmund operator
• multilinear fractional integral operator
• tent space