TRIEBEL-LIZORKIN-MORREY SPACES ASSOCIATED WITH NONNEGATIVE SELF-ADJOINT OPERATOR

Abstract

Let L be a nonnegative self-adjoint operator on 2()nL with a heat kernel satisfying a Gaussian upper bound. In this work, we introduce Triebel-Lizorkin-Morrey spaces ,L,()npqFMα associated with the operator L for the entire range 0,,pq<≤∞α∈. We then prove that our new spaces satisfy important features such as continuous characterizations in terms of square functions, or atomic decomposition.