论文标题
多线性ra-brascamp-lieb不平等的测试条件
Testing conditions for multilinear Radon-Brascamp-Lieb inequalities
论文作者
论文摘要
本文为一类多线性功能的$ l^p $结合性建立了必要的条件，其中包括Brascamp-lieb不平等和与代数发病率关系相关的广义ra不平等。测试条件涉及沿相关投影的纤维的某些雅各布型量的逆权力的平均值，并涵盖了许多广泛研究的特殊情况，包括对非平滑性超曲面或非平滑曲线进行的衡量。证明的核心是基于古斯（Guth）在一个方向上的可见性引理以及对另一个方向的仔细分析。讨论了各种应用，这些应用证明了曲率和横向性之间的新的微妙相互作用，并在模型案例中建立了非平凡的混合 - $ l^p $ - 提高不平等现象，并在抛物线上使用仿射性超表面度量。
This paper establishes a necessary and sufficient condition for $L^p$-boundedness of a class of multilinear functionals which includes both the Brascamp-Lieb inequalities and generalized Radon transforms associated to algebraic incidence relations. The testing condition involves bounding the average of an inverse power of certain Jacobian-type quantities along fibers of associated projections and covers many widely-studied special cases, including convolution with measures on nondegenerate hypersurfaces or on nondegenerate curves. The heart of the proof is based on Guth's visibility lemma in one direction and on a careful analysis of Knapp-type examples in the other. Various applications are discussed which demonstrate new and subtle interplay between curvature and transversality and establish nontrivial mixed-norm $L^p$-improving inequalities in the model case of convolution with affine hypersurface measure on the paraboloid.
