Weighted norm inequalities, Gaussian bounds and sharp spectral multipliers

Analysis Seminar
Tuesday, December 8, 2009 - 16:00
1 hour (actually 50 minutes)
Skiles 269
Macquarie University
In this talk,we study  weighted L^p-norm inequalities  for general spectralmultipliersfor self-adjoint positive definite operators on L^2(X), where X is a space of homogeneous type. We show that the sharp weighted Hormander-type spectral multiplier theorems  follow  from the appropriate estimatesof the L^2 norm of the kernel of spectral multipliers and the Gaussian boundsfor the corresponding heat kernels. These results are applicable to spectral multipliersfor group invariant  Laplace operators acting on Lie groups of polynomialgrowth and   elliptic operators on compact manifolds. This is joint work with Adam Sikora and Lixin Yan.