Adyghe Int. Sci. J. Vol. 23. No 1. P. 20-27
Read article Contents of this issue
|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: https://orcid.org/0000-0002-8415-9822, firstname.lastname@example.org
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 author are thankful to the anonymous reviewer for his valuable remakes.
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.
DOI: https://doi.org/10.47928/1726-9946-2023-23-l-20-27; EDN: BLNHRE
The author has 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.
This work is licensed under a Creative Commons Attribution 4.0 License.