On multilinear spectral cluster estimates for manifolds with boundary

• Autores: Matthew D. Blair, Hart F. Smith, Christopher D. Sogge
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 2-3, 2008, págs. 419-426
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n3.a2
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• Resumen

  • 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, G\'erard, 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.