Bavrin\u2019s Type Factorization of the Temljakov Operator for Holomorphic Functions in Circular Domains of mathbb {C}^{n}

Abstract

The paper concerns investigations of holomorphic functions of several complex variables with a factorization of their Temljakov transform. Firstly, there were considered some inclusions between the families mathcal {C}_{mathcal {G}},mathcal {M}_{mathcal {G}},mathcal {N}_{mathcal {G}},mathcal {R}_{mathcal {G}},mathcal {V}_{mathcal {G}} of such holomorphic functions on complete n-circular domain mathcal {G} of mathbb {C}^{n} in some papers of Bavrin, Fukui, Higuchi, Michiwaki. A motivation of our investigations is a condensation of the mentioned inclusions by some new families of Bavrin’s type. Hence we consider some families mathcal {K}_{ mathcal {G}}^{k},kge 2, of holomorphic functions f : mathcal {G}rightarrow mathbb {C},f(0)=1, defined also by a factorization of mathcal {L}f onto factors from mathcal {C}_{mathcal {G}} and mathcal {M} _{mathcal {G}}. We present some interesting properties and extremal problems on mathcal {K}_{mathcal {G}}^{k}.