Some propositonerties of a Bavrin’s family of holomorphic functions in Cn

Abstract

In the [1], [4], [3] and [2] there were examined the Bavrin?s families (of holomorphic functions on bounded complete n? circular domains G ?Cn) in which the Temljakov operator Lf was presented as a product of a holomorphic function h with a positive real part and the (0, k)?symmetrical part of the function f,(k ? 2 is a positive integer). In [17] there was investigated the family of the above mentioned type, where the operator LLf was presented as a product of the same function h ? CG and (0, 2)-symmetrical part of the operator Lf. These considerations can be completed by the case of the factorization LLf by the same function h and the (0, k)-symmetrical part of operator Lf. In this article we will discuss the above case. In particular, we will present some estimates of a generalization of the norm of m-homogeneous polynomials Qf,m in the expansion of function f and we will also give a few relations between the different Bavrin?s families of the above kind.