Oscillating spectral multipliers on Riemannian manifolds
Athanasios G. Georgiadis · Analysis · 2015
Abstract Suppose that M is a Riemannian manifold satisfying the doubling volume property. Let L be a self-adjoint positive definite operator on M. We consider the heat semigroup e - t L $e^{-tL}$ and we assume that the associated heat kernel p t ( x , y ) $p_{t}(x,y)$ satisfies certain upper Gaussian estimates. We study the Lp boundedness of oscillating spectral multipliers m α , β ( L ) $m_{\alpha ,\beta }(L)$ .