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23_1_Shamoyan R. F., Tomashevskaya E. B.

Adyghe Int. Sci. J. Vol. 23. No 1. P. 20-27

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MSC 32А07, 432А10 Original Article

On the action of Toeplits operators into new BMOA type spaces in the unit disk

Romi Fayzovich Shamoyan
Ph.D. (Phys. & Math.), Senior Researcher, Bryansk State Technical University (Bryansk, Russia), ORCID:,  
Elena Bronislavovna Tomashevskaya
Ph. D. (Phys. & Math.), Associate Professor of the Department of Higher Mathematics, Bryansk State Technical University (Bryansk, Russia)

Abstract. We provide new sharp results on the action of Toeplitz operators from Triebel and Besov spaces to new BMOA-type function spaces on the unit disk. We modify little our previously known proofs. We show our theorems using standard estimates of complex function theory. The proof of sufficiency and neccesity parts of our theorems follow the same type arguments as in previous already known cases. In particular we use standart test function for the proof of neccesity part and the same line of arguments as in previous already known cases. Our theorems may have many applications in complex function theory. Previously such type theorems were known in less general classses of BMOA type in the unit disk.
Keywords: Toeplitz operators, Besov type spaces, analytic functions, unit disk, BMOA type spaces

Acknowledgments: the authors are thankful to the anonymous reviewer for his valuable remakes.
The authors declare no conflict of interest.

For citation. Shamoyan R. F., Tomashevskaya E. B. On the action of Toeplits operators into new BMOA type spaces in the unit disk. Adyghe Int. Sci. J. 2023. Vol. 23, No. 1. P. 20-27.

The authors have read and approved the final version of the manuscript.
Submitted 10.11.2022; approved after reviewing 27.02.2023; accepted for publication 17.03.2023

                                                                                                                                         © Shamoyan R. F.
                                                                                                                                                                     Tomashevskaya E. B., 2023


1. Shamoyan R. F. Generalized Hardy transformation and Toeplits operators in BMOA-type function spaces in the unit disk. Ukrainian Math. Jour. Vol. 53 (2001). Pp. 1260-1274.
2. Aleksandrov A. B., Beller V. V. Hankel operators and similarity to a contraction, hit. Math. Res. Notices. 6 (1996). Pp. 264-275.
3. Janson S., Petre J., Semmes S. On the action of Hankel and Toeplitz operators on some function spaces Duke. Math. Jour. 51 (1984), No. 4. Pp. 937-957.
4. Ortega J., Fabrega J. Holomorphic Tricbcl-Lizorkin spaces, Jour. Funct. Anal. 151(1) (1997). Pp. 177-212.
5. Ortega J., Fabrega J. Pointwise multipliers and corona type decomposition in BMOA, Ann Inst. Fourier, 46, No. 1 (1996). Pp. 111-137.
6. Shamoyan R. F. Multipliers, Toeplitz operators and duality in some spaces of analytic functions in the unit polydisk. PhD Dissertation, Moscow, (2001).
7. Aleksandrov A. B. Function Theory in the Ball, in Several Complex Variables II, Springer-Vcrlag, New York, (1994).
8. Harutyunyan A., Shamoyan F. Toeplitz operators in multidimensional spaces Hp(a) of M. M. Djrbashian. Jour, of Contcmp. Math. An., National Ac. of Sei. of Armenia 30(2) (1995). Pp. 70-78.
9. Shamoyan R. F. On multipliers from Bergman-type spaces to Hardy spaces in the polydisk, Ukrainian Math. Jour. 10 (2000). Pp. 1405-1415.

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