Inequality to describe double Carleson measure and description of Carleson inverse inequality

Based on the definition of the Carleson measure with αorder (α0) αnd related operator theory, a study is performed on the Carleson measure. An integral inequality theorem on double Carleson measure is obtained, and by expansion of the Lemma 1, an inverse inequality theorem is deduced to describe the Carleson measure μ with αorder (α0) under a certain condition. Furthermore, a discussion is made on the combination of the Carleson inverse inequality with higherorder derivatives.