Adyghe Int. Sci. J. Vol. 23, No 2. P. 18–26
|MSC 32А07, 432А10||Original Article|
On Bergman type projections in bounded strongly pseudoconvex domains
Romi Fayzovich Shamoyan
Cand.Sci. (Phys. & Math.), Associate Professor, Higher Mathematics Department, Bryansk State Technical University (241035, Russia, Bryansk, 10-B Kharkovskaya St.), ORCID: https://orcid.org/0000-0002-8415-9822, firstname.lastname@example.org
Elena Bronislavovna Tomashevskaya
Cand.Sci. (Phys. & Math.), Associate Professor of Higher Mathematics Department, Bryansk State Technical University (241035, Russia, Bryansk, 10-B Kharkovskaya St.), ORCID: https://orcid.org/0000-0002-1314-0550, email@example.com
Abstract. In our note we prove the boundedness of Bergman type projections in two different spaces of analytic functions with mixed norm in general bounded strongly pseudoconvex domains with smooth boundary.The first class of analytic functions was studied previously by many authors,the second function space hovewer is completely new.
Our proofs are based on standard known estimates of function space theory in bounded strongly pseudoconvex domains with smooth boundary and on some known estimates of Bergman kernel in such type domains. These estimates are also well- known in the unit disk.This allows us to provide proofs first in one dimensional case which are simpler and then repeating same arguments to show same type results also in more general situation. Note that many results on boundedness of Bergmam type projections are well known and they have also various nice applications in complex function theory in one or several complex variable. Our results may also have various applications in complex function theory in bounded strongly pseudoconvex domains with smooth boundary.
Keywords: pseudoconvex domains, unit disk, analytic function, Bergman projection
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. 2. P. 18-26.
DOI: https://doi.org/10.47928/1726-9946-2023-23-2-18-26; EDN: SALPHL
The authors have read and approved the final version of the manuscript.
Submitted 01.06.2023; approved after reviewing 09.06.2023; accepted for publication 15.06.2023
© Shamoyan R. F.
Tomashevskaya E. B., 2023
1. J. Ortega, J. Fabrega Mixed norm spaces and interpolation. Studia Math., 109 (3), (1994), 233-254.
2. R. F. Shamoyan, E. B. Tomashevskaya On new sharp theorems for multyfunctional BMOA type spaces in bounded strongly pseudoconvex domains. Vestnik KRAUNC. Fiz.-mat. nauki. 2020, 32: 3, 102-113. DOI: 10.26117/2079-6641-2020-32-3-102-113
3. R. F. Shamoyan, E. B. Tomashevskaya. On new decomposition theorems in some analytic function spaces in bounded strongly pseudoconvex domains, Jour. Siberian Fed. University, 2020. 13-4, 503-514.
4. F. Jr. Beatrous L^p estimates for extensions of holomorphic functions, Michigan Math. J. 32(3), (1985), 543-565.
5. M. Abate, J. Raissy, A. Sarraco Toeplitz operators and Carleson measures in strongly pseudoconvex domains. J. Funct Analysis 263(11), (2012), 3449-3491.
6. P. Ahern, R. Schneider Holomorphic Lipschitz functions in pseudoconvex domains, Amer J. Math. 101(3), (1979), 543-565. Published 1 june 1979 Mathematics
7. M. Peloso Hankel operators on weighted Bergman spaces on strongly pseudoconvex domains, Illinois J. Math., 38(2), (1994), 223-249.
This work is licensed under a Creative Commons Attribution 4.0 License.