The paper concerns holomorphic functions in complete bounded n-circular domains $${{\mathcal {G}}}$$ of the space $${\mathbb {C}}^n$$. The object of the present investigation is to solve majorization problem of Temljakov operator. This type of problem has been studied earlier in Liczberski and Żywien (Folia Sci Univ Tech Res 33:37–42, 1986), Liczberski (Bull Technol Sci Univ Łodź 20:29–37, 1988) and Leś-Bomba and Liczberski (Demonstratio Math 42(3):491–503, 2009). In this paper we considered the family $${{\mathcal {M}}}_{{{\mathcal {G}}}}\cap {{\mathcal {F}}}_{0,k}({{\mathcal {G}}})$$, i.e. the functions of the Bavrin family $${{\mathcal {M}}}_{{{\mathcal {G}}}}$$, which are (0, k)-symmetrical.

中文翻译：

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$${\mathbb {C}}^n$$Cn 中 Bavrin 家族的 Temljakov 算子的专业化

该论文涉及空间 $${\mathbb {C}}^n$$ 的完整有界 n 圆形域 $${{\mathcal {G}}}$$ 中的全纯函数。本研究的目的是解决Temljakov算子的专业化问题。Liczberski 和 Żywien（Folia Sci Univ Tech Res 33:37–42, 1986）、Liczberski（Bull Technol Sci Univ Łodź 20:29–37, 1988）和 Leś-Bomba 和 LDemostr数学 42(3):491–503, 2009)。在本文中，我们考虑了家庭 $${{\mathcal {M}}}_{{{\mathcal {G}}}}\cap {{\mathcal {F}}}_{0,k}({{ \mathcal {G}}})$$，即 Bavrin 家族 $${{\mathcal {M}}}_{{{\mathcal {G}}}}$$ 的函数，即 (0, k )-对称。