Contents Online
Mathematical Research Letters
Volume 15 (2008)
Number 3
On multilinear spectral cluster estimates for manifolds with boundary
Pages: 419 – 426
DOI: https://dx.doi.org/10.4310/MRL.2008.v15.n3.a2
Authors
Abstract
We prove bilinear and trilinear estimates for the spectral cluster operator on two and three-dimensional compact manifolds with boundary. These are the natural analogs of earlier estimates for the boundaryless case of Burq, Gérard, and Tzvetkov~\cite{bgtbilin}, \cite{bgtmultilin}. Our theorem reduces to establishing inequalities over small cubes whose size depends on frequency. After rescaling, these inequalities follow from mixed $L^p$ norm estimates on squarefunctions associated to the wave equation.
Published 1 January 2008