The coefficient multipliers on $ H^2 $ and $ \mathcal{D}^2 $ with Hyers–Ulam stability

Chun Wang; Chun Wang

doi:10.3934/math.2024614

AIMS Mathematics

2024, Volume 9, Issue 5: 12550-12569. doi: 10.3934/math.2024614

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Research article

The coefficient multipliers on $ H^2 $ and $ \mathcal{D}^2 $ with Hyers–Ulam stability

Chun Wang ^,

Department of Mathematics, Changzhi University, Changzhi 046011, China

Received: 20 February 2024 Revised: 17 March 2024 Accepted: 22 March 2024 Published: 01 April 2024
MSC : 39B72, 39B82, 47B91

In this paper, we investigated the Hyers–Ulam stability of the coefficient multipliers on the Hardy space $ H^2 $ and the Dirichlet space $ \mathcal{D}^2 $. We also investigated the Hyers–Ulam stability of the coefficient multipliers between Dirichlet and Hardy spaces. We provided the necessary and sufficient conditions for the coefficient multipliers to have Hyers–Ulam stability on Hardy space $ H^2 $, on Dirichlet space $ \mathcal{D}^2 $, and between Dirichlet and Hardy spaces. We also showed that the best constant of Hyers–Ulam stability exists under different circumstances. Moreover, some illustrative examples were discussed.
- Hyers–Ulam stability,
- coefficient multipliers,
- Dirichlet spaces,
- Hardy spaces
Citation: Chun Wang. The coefficient multipliers on $ H^2 $ and $ \mathcal{D}^2 $ with Hyers–Ulam stability[J]. AIMS Mathematics, 2024, 9(5): 12550-12569. doi: 10.3934/math.2024614

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Abstract

In this paper, we investigated the Hyers–Ulam stability of the coefficient multipliers on the Hardy space $ H^2 $ and the Dirichlet space $ \mathcal{D}^2 $. We also investigated the Hyers–Ulam stability of the coefficient multipliers between Dirichlet and Hardy spaces. We provided the necessary and sufficient conditions for the coefficient multipliers to have Hyers–Ulam stability on Hardy space $ H^2 $, on Dirichlet space $ \mathcal{D}^2 $, and between Dirichlet and Hardy spaces. We also showed that the best constant of Hyers–Ulam stability exists under different circumstances. Moreover, some illustrative examples were discussed.

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