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Some remarks on Blaschke type products in large area Nevanlinna spaces in the unit disk

https://doi.org/10.25587/SVFU.2023.13.41.008

Аннотация

The intention of this paper is to introduce and study certain new analytic spaces in the disk and to show that certain Blaschke type products belong to new large Nevanlinna type classes in the unit disk. We also provide parametric representation of such classes. These results extend and complement some previously known assertions of this type obtained earlier by other authors. Our arguments are based on certain new embeddings which relate the well-known Sp α area Nevanlinna spaces in the unit disk with our new large area Nevanlinna type spaces in the unit disk.

Об авторах

R. Shamoyan
Bryansk State University
Россия

Romi Shamoyan

14 Bezhitskaya Street, 241023 Bryansk



O. Mihi´c
University of Belgrade, Faculty of Organizational Sciences
Сербия

Olivera Mihi´c

154 Jove Ili´ca Street, Belgrade



Список литературы

1. Hayman W., Meromorphic Functions, Oxford Univ. Press, Oxford (1964).

2. Djrbashian M. M. and Shamoian F. A., Topics in the Theory of Ap α Spaces, Teubner, Leipzig (1988).

3. Djrbashian M. M., Integral Transforms and Representation of Functions in Complex Plane [in Russian], Nauka, Moscow (1966).

4. Shamoyan F. A. and Shubabko E. N., “Parametric representations of some classes of holomorphic functions in the disk,” in: Complex Analysis, Operators and Related Topics, pp. 331– 338, Birkh¨auser, Basel (2000) (Oper. Theory, Adv. Appl., vol. 113).

5. Bergh J. and Lofstrom J., Interpolation Spaces, Springer, New York (1976).

6. Shamoyan F. A., “Parametric representation and description of the root sets of weighted classes of functions holomorphic in the disk,” Sib. Math. J., 40, No. 6, 1211–1229 (1999).

7. Shamoyan R. and Li H., “Descriptions of zero sets and parametric representations of certain analytic area Nevanlinna type classes in disk,” Proc. Razmadze Math. Inst., 151, 103–108 (2009).

8. Shamoyan R. and Mihi´c O., “On zero sets and embeddings of some new analytic function spaces in the unit disc,” Kragujevac J. Math., 38, No. 2, 229–244 (2014).

9. Shamoyan R. and Mihi´c O., “On zeros of some analytic spaces of area Nevanlinna type in a halfplane,” Tr. Petrozavodsk. Gos. Univ., Ser. Mat., 17, 67–72 (2010).

10. Shamoyan R. and Arsenovi´c M., “On zero sets and parametric representations of some new analytic and meromorphic function spaces in the unit disk,” Filomat, 25, No. 3, 1–14 (2011).

11. Djrbashian M. M. and Zakharyan V., Classes and Boundary Properties of Functions That are Meromorphic in the Disk [in Russian], Nauka, Moscow (1993).

12. Shvedenko S. V., “Hardy classes and related spaces of analytik functions in the unit disk, polydisc and unit ball,” Itogi Nauki i Tekhniki, Ser. Mat., VINITI, Moscow (1985).

13. Shamoyan R. and Li H., “Descriptions of zero sets and parametric representations of certain analytic area Nevanlinna type classes in the unit disk,” Kragujevac J. Math., 34, 73–89 (2010).

14. Jevti´c M., Pavlovi´c M., and Shamoyan R., “A note on diagonal mapping theorem in spaces of analytic functions in the unit polydisk,” Publ. Math. Debrecen, 74, No. 1-2, 1–14 (2009).

15. Shamoyan R. F., “On multipliers from Bergman type spaces into Hardy spaces in the polydisc [in Russian],” Ukr. Math. J., 10, 1405–1415 (2000).


Рецензия

Для цитирования:


Shamoyan R., Mihi´c O. Some remarks on Blaschke type products in large area Nevanlinna spaces in the unit disk. Математические заметки СВФУ. 2023;30(3):78-90. https://doi.org/10.25587/SVFU.2023.13.41.008

For citation:


Shamoyan R., Mihi´c O. Some remarks on Blaschke type products in large area Nevanlinna spaces in the unit disk. Mathematical notes of NEFU. 2023;30(3):78-90. (In Russ.) https://doi.org/10.25587/SVFU.2023.13.41.008

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ISSN 2411-9326 (Print)
ISSN 2587-876X (Online)