Volume no :7, Issue no: 2, February (2011)

Journal of Mathematical Sciences: Advances and Applications

MIKHLIN-HÖRMANDER THEOREM FOR HIGHER ORDER DIFFERENTIAL OPERATORS ON RIEMANNIAN MANIFOLDS

Author's: Athanasios G. Georgiadis
Pages: [115] - [132]
Received Date: February 28, 2011
Submitted by:

Abstract

Let M be a Riemannian manifold, which satisfies the doubling volume property. Let L be a 2m-order differential operator on M and a multiplier satisfying the Mikhlin-Hörmander condition. We also assume that the associated heat kernel satisfies a certain upper Gaussian estimate, and we prove that the spectral multiplier is bounded on and from to week.

Keywords

spectral multipliers, higher order differential operators, heat kernels, Riemannian manifolds, Calderon Zygmund decomposition, Hardy-Littlewood maximal function.