$L^p$ improving properties and maximal estimates for certain multilinear averaging operators

Abstract

In this article we focus on $L^p$ estimates for two types of multilinear lacunary maximal averages over hypersurfaces with curvature conditions. Moreover, we give a different proof for the bilinear lacunary spherical maximal functions. To obtain our results, we make use of the $L^1$-improving estimates of multilinear averaging operators. We also obtain $L^p$-improving estimates for certain multilinear averages by means of the nonlinear Brascamp-Lieb inequality.

32 pages. There was an error in proof of Theorem 1.5, so we added an assumption to fix it. Typos and symbolic errors were also fixed