$L^p$ improving multilinear Radon-like transforms

Abstract

We characterize (up to endpoints) the $k$-tuples $(p_1,\dots ,p_k)$ for which certain $k$-linear generalized Radon transforms map $L^{p_1}\times \cdots \times L^{p_k}$ boundedly into $\mathbb{R}$. This generalizes a result of Tao and Wright.

This is a preprint version of a published article. The final version is in Rev. Mat. Ibero. 27 (2011), no. 3, 1059-1085

References in corpus (2)

• A convolution estimate for two-dimensional hypersurfaces
• Endpoint bounds for a generalized {R}adon transform