New Atomic Decomposition for Besov Type Space dot{B}^0_{1,1} Associated with Schrödinger Type Operators

Abstract

Let (X, d, mu ) be a space of homogeneous type. Let L be a nonnegative self-adjoint operator on L^2(X) satisfying certain conditions on the heat kernel estimates which are motivated from the heat kernel of the Schrödinger operator on mathbb {R}^n. The main aim of this paper is to prove a new atomic decomposition for the Besov space dot{B}^{0, L}_{1,1}(X) associated with the operator L. As a consequence, we prove the boundedness of the Riesz transform associated with L on the Besov space dot{B}^{0, L}_{1,1}(X).