# The Bohr Inequality for the Generalized Cesáro Averaging Operators

@article{Kayumov2021TheBI, title={The Bohr Inequality for the Generalized Ces{\'a}ro Averaging Operators}, author={Ilgiz R. Kayumov and Diana Khammatova and Saminathan Ponnusamy}, journal={Mediterranean Journal of Mathematics}, year={2021} }

∞ n=0 |an| (1/3) = 1 if and only if f is a constant function. However, there are a lot of generalizations and extensions of this theorem (cf. [12–14, 29]). The interest on this topic was revived due to the discovery of extensions to domains in C and to more general abstract setting in various contexts, due mainly to works of Aizenberg, Boas, Khavinson, and others (cf. [2–4, 8, 10, 25]). In [2, 4], multidimensional analogues of Bohr’s inequality in which the unit disk D is replaced by a domain…

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## References

SHOWING 1-10 OF 36 REFERENCES

### Cesàro averaging operators

- Mathematics
- 2003

We define a family of Cesàro operators $ {\cal C} ^{\vec \gamma} $ on the polydisc Un, and consider the question of its boundedness on some spaces of analytic functions.

### On the Bohr inequality for the Cesáro operator

- Mathematics
- 2020

We investigate an analog of Bohr’s results for the Cesáro operator acting on the space of holomorphic functions defined on the unit disk. The asymptotical behaviour of the corresponding Bohr sum is…

### New Inequalities for the Coefficients of Unimodular Bounded Functions

- Mathematics
- 2020

The classical inequality of Bohr asserts that if a power series converges in the unit disk and its sum has modulus less than or equal to 1, then the sum of absolute values of its terms is less than…

### Refined Bohr inequality for bounded analytic functions

- MathematicsBulletin des Sciences Mathématiques
- 2021

### Improved Bohr's phenomenon in quasi-subordination classes

- MathematicsJournal of Mathematical Analysis and Applications
- 2022