Testing conditions for multilinear Radon-Brascamp-Lieb inequalities
The partial differential equations and analysis seminar is the research seminar associated with the applied and nonlinear analysis, and the analysis and geometry programs.
Abstract: We will discuss a new necessary and sufficient testing 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 Zoom link for this talk is available here. If you are not currently affiliated with the ANU, please contact Po-Lam Yung for access.