Some properties of a Bavrin's family of holomorphic functions in C^n

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  in C^n)
in which the Temljakov operator Lf was presented as a product of a holo-
morphic 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 in-
vestigated the family of the above mentioned type, where the operator
LLf was presented as a product of the same function h in C_G 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 Q_f,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.