Lᵖ improving properties and maximal estimates for certain multilinear averaging operators

In this article we focus on Lᵖ 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 L¹ -improving estimates of multilinear averaging operators. We also obtain Lᵖ -improving estimates for certain multilinear averages by means of the nonlinear Brascamp–Lieb inequality.