OPERATOR-VALUED FOURIER MULTIPLIER THEOREMS ON TRIEBEL SPACES

摘要

The authors establish operator-valued Fourier multiplier theorems on Triebelspaces on RN , where the required smoothness of the multiplier functions depends on thedimension N and the indices of the Triebel spaces. This is used to give a su?cient conditionof the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problemswith Dirichlet boundary conditions.