空间 $A^2$ 和 $\mathcal{D}^2$ 上具有 Hyers-Ulam 稳定性的系数乘子

Abstract

Abstract:

In this paper, Hyers-Ulam stability of the coefficient multipliers between Bergman space $A^2$ and Dirichlet space $\mathcal{D}^2$ are investigated. Some sufficient conditions which for that a complex sequence $\lambda=\{\lambda_n\}_{n=0}^\infty$ can be the coefficient multiplier between Bergman space $A^2$ and Dirichlet space $\mathcal{D}^2$ are given. Some necessary and sufficient conditions for that the coefficient multipliers have the Hyers-Ulam stability between Bergman space $A^2$ and Dirichlet space $\mathcal{D}^2$ are also given. This paper also show that the best constant of Hyers-Ulam stability exists under different circumstances. Moreover, some illustrative examples are also discussed.

Key words: coefficient multipliers, Hyers-Ulam stability, Dirichlet spaces, Bergman spaces

CLC Number:

O177.9

Chun Wang, Tianzhou Xu. The Coefficient Multipliers Between $A^2$ and $\mathcal{D}^2$ with Hyers-Ulam Stability[J].Acta mathematica scientia,Series A, 2025, 45(5): 1381-1391.

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The Coefficient Multipliers Between $A^2$ and $\mathcal{D}^2$ with Hyers-Ulam Stability

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