Generalized Bohr inequalities for K-quasiconformal harmonic mappings and their applications
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915932534734848 |
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| author | Biswas, Raju Mandal, Rajib |
| author_facet | Biswas, Raju Mandal, Rajib |
| contents | The classical Bohr theorem and its subsequent generalizations have become active areas of research, with investigations conducted in numerous function spaces. Let $\{ψ_n(r)\}_{n=0}^\infty$ be a sequence of non-negative continuous functions defined on $[0,1)$ such that the series $\sum_{n=0}^\infty ψ_n(r)$ converges locally uniformly on the interval $[0, 1)$. The main objective of this paper is to establish several sharp versions of generalized Bohr inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings on the unit disk $\D := \{z \in \mathbb{C} : |z| < 1\}$. To achieve these, we employ the sequence of functions $\{ψ_n(r)\}_{n=0}^\infty$ in the majorant series rather than the conventional dependence on the basis sequence $\{r^n\}_{n=0}^\infty$. As applications, we derive a number of previously published results as well as a number of sharply improved and refined Bohr inequalities for harmonic mappings in $\D$. Moreover, we obtain a convolution counterpart of the Bohr theorem for harmonic mapping within the context of the Gaussian hypergeometric function |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Bohr inequalities for K-quasiconformal harmonic mappings and their applications Biswas, Raju Mandal, Rajib Complex Variables 30A10, 30B10, 30C62, 30C75, 40A30 The classical Bohr theorem and its subsequent generalizations have become active areas of research, with investigations conducted in numerous function spaces. Let $\{ψ_n(r)\}_{n=0}^\infty$ be a sequence of non-negative continuous functions defined on $[0,1)$ such that the series $\sum_{n=0}^\infty ψ_n(r)$ converges locally uniformly on the interval $[0, 1)$. The main objective of this paper is to establish several sharp versions of generalized Bohr inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings on the unit disk $\D := \{z \in \mathbb{C} : |z| < 1\}$. To achieve these, we employ the sequence of functions $\{ψ_n(r)\}_{n=0}^\infty$ in the majorant series rather than the conventional dependence on the basis sequence $\{r^n\}_{n=0}^\infty$. As applications, we derive a number of previously published results as well as a number of sharply improved and refined Bohr inequalities for harmonic mappings in $\D$. Moreover, we obtain a convolution counterpart of the Bohr theorem for harmonic mapping within the context of the Gaussian hypergeometric function |
| title | Generalized Bohr inequalities for K-quasiconformal harmonic mappings and their applications |
| topic | Complex Variables 30A10, 30B10, 30C62, 30C75, 40A30 |
| url | https://arxiv.org/abs/2411.01837 |