The paper is devoted to the study of relations between the following differential operators in the space , of holomorphic functions in the unit polydisc :
Here, belongs to or for some , , . The authors goal is to reduce the study of to a study of , which were studied by many authors. An example of a result is the following.
Theorem 2.7. Let , , and . If for or for and , then
From here some new embedding theorems for various quasinorms, where the operators are participating, are obtained.