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

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.