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

Renata Długosz ; Piotr Liczberski ; Agnieszka Sibelska ; Edyta Trybucka

Filomat, Tome 36 (2022) no. 6, p. 2073

Résumé

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 L f 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 LL f was presented as a product of the same function h ∈ C G and (0, 2)-symmetrical part of the operator L f. These considerations can be completed by the case of the factorization LL f by the same function h and the (0, k)-symmetrical part of operator L f. 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.

Détail

DOI : 10.2298/FIL2206073D

Classification : 32A30, 30C45
Keywords: holomorphic functions of several complex variables, complete n-circular domains, the Minkowski function, the Temljakov operator, Bavrin’s families, G-balance of k-homogeneous polynomials