Improved curvature conditions on L2 × ⋯ × L2 → L2/ bounds for multilinear maximal averages

This is the authors' abstract. We don't add key points for this paper.

In this article, we focus on L 2 ( R d ) × ⋯ × L 2 ( R d ) → L 2 / m ( R d ) estimates for multilinear maximal averages over non-degenerate hypersurfaces. Our findings is new for m -linear averages with m ≥ 3 , and represent a reproof of the recent result of T. Borges, B. Foster, and Y. Ou on the curvature conditions of the hypersurfaces required in establishing L 2 ( R d ) × L 2 ( R d ) → L 1 ( R d ) estimates of bilinear maximal functions.