Triebel-Lizorkin Spaces Estimates for Evolution Equations with Structure Dissipation

Abstract

This work is concerned with the long time decay estimates of the generalized heat equations and the generalized wave equations in the homogeneous Triebel-Lizorkin spaces. We first extend the known results for the generalized heat equations in the real Hardy spaces. We also extend the known results for the generalized wave equations with structure dissipation in the real Hardy spaces. The main tools employed are the decomposition of the unit, duality property in Triebel-Lizorkin spaces and the multiplier theorems in different function spaces such as Lebesgue spaces, real Hardy spaces and Triebel-Lizorkin spaces.