Affiliation:
1. Łódź University of Technology
2. University of Łódź
3. University of Rzeszów
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.
Publisher
National Library of Serbia
Reference18 articles.
1. I. I. Bavrin, A class of regular bounded functions in the case of several complex variables and extreme problems in that class, Moskov Oblast. Ped. Inst., Moscow (1976), 1-96, (in Russian).
2. R. Długosz, Embedding theorems for holomorphic functions of several complex variables, J. Appl. Anal., 19, (2013), 153-165.
3. R. Długosz, E. Leś, Embedding theorems and extremal problems for holomorphic functions on circular domains of Cn Complex Var. Elliptic Equ., 59(6)(2014), 883-899.
4. R. Długosz, P. Liczberski, An application of hypergeometric functions to a construction in several complex variables, J. Anal. Math., (2019) 707-721.
5. R. Długosz, E. Leś, A. Sibelska, A new inclusion for Bavrin’s families of holomorphic functions in bounded comlete n-circular domains, Math.Slovaca, 66(4) (2016), 1-7.