Geodesic
Characterization of weighted mixed norm spaces of analytic functions defined in terms of conditions on the Fourier coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2022), pp. 57-64.

Voir la notice de l'article provenant de la source Math-Net.Ru

The purpose of this paper is to study a certain class of functional sequences and apply the results obtained to the description of functional spaces of analytic functions with mixed norm on the unit disk of the complex plane, defined in terms of conditions on the Fourier coefficients.
Keywords: spaces with mixed norm, spaces of analytic functions. 
@article{IVM_2022_1_a4,
     author = {A. N. Karapetyants and I. Yu. Smirnova},
     title = {Characterization of weighted mixed norm spaces of analytic functions defined in terms of conditions on the {Fourier} coefficients},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {57--64},
     publisher = {mathdoc},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_1_a4/}
}
TY  - JOUR
AU  - A. N. Karapetyants
AU  - I. Yu. Smirnova
TI  - Characterization of weighted mixed norm spaces of analytic functions defined in terms of conditions on the Fourier coefficients
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2022
SP  - 57
EP  - 64
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2022_1_a4/
LA  - ru
ID  - IVM_2022_1_a4
ER  - 
%0 Journal Article
%A A. N. Karapetyants
%A I. Yu. Smirnova
%T Characterization of weighted mixed norm spaces of analytic functions defined in terms of conditions on the Fourier coefficients
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2022
%P 57-64
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2022_1_a4/
%G ru
%F IVM_2022_1_a4
A. N. Karapetyants; I. Yu. Smirnova. Characterization of weighted mixed norm spaces of analytic functions defined in terms of conditions on the Fourier coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2022), pp. 57-64. http://geodesic.mathdoc.fr/item/IVM_2022_1_a4/

[1] Bergman S., “Uber die kernfunctionen eines bereiches und verhalten am rande, I”, J. Reine Agnew. Math., 169 (1933), 1–42 | MR

[2] Dzhrbashyan M. M., “O kanonicheskom predstavlenii funktsii, meromorfnykh v edinichnom kruge”, Dokl. AN Armenii SSR, 3:1 (1945), 3–9 | MR

[3] Dzhrbashyan M. M., “O probleme predstavimosti analiticheskikh funktsii”, Soobsch. In-ta matem. i mekhan. AN Arm. SSR, 2 (1948), 3–40

[4] Djrbashian A. E., Shamoian F. A., Topics in the theory of $A^p_\alpha$ spaces, Teubner-Texte zur Math., 105, Leipzig, 1988 | MR

[5] Duren P., Schuster A., Bergman spaces, Math. Sur. and Monographs, 100, American Math. Soc., Providence, RI, 2004 | DOI | MR | Zbl

[6] Shamoyan F. A., Vesovye prostranstva analiticheskikh funktsii so smeshannoi normoi, RIO, BGU, Bryansk, 2014

[7] Zhu K., Operator theory in function spaces, Monographs and textbooks in Pure and Appl. Math., Marcel Dekker, New York, 1990 | MR | Zbl

[8] Zhu K., Spaces of holomorphic functions in the unit ball, Graduate texts in Math., Springer, New York, 2004 | MR

[9] Karapetyants A., Taskinen J., “Toeplitz operators with radial symbols on weighted holomorphic Orlicz space”, Operator Algebras, Toeplitz Operators and Related Topics, Operator Theory: Advances and Appl., 279, eds. Bauer W. et al., 2020 | MR

[10] Karapetyants A. N., Samko S. G., “On Grand and Small Bergman Spaces”, Math. Notes, 104:3 (2018), 439–446 | MR | Zbl

[11] Karapetyants A., Rafeiro H., Samko S., “Boundedness of the Bergman projection and some properties of Bergman type spaces”, Complex Anal. and Operator Theory, 2018, 1–15 | MR

[12] Karapetyants A., Samko S., “On boundedness of Bergman projection operators in Banach spaces of holomorphic functions in half plane and harmonic functions in half space”, J. Math. Sci., 226:4 (2017), 344–354 | DOI | MR | Zbl

[13] Karapetyants A. N., Samko S. G., “On mixed norm Bergman–Orlicz–Morrey spaces”, Georgian Math. J., 25:2 (2018), 271–282 | DOI | MR | Zbl

[14] Karapetyants A., Samko S., “Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces”, Fract. Calc. Appl. Anal., 2017, no. 5, 1106–1130 | DOI | MR | Zbl

[15] Karapetyants A., Samko S., “Mixed norm Bergman–Morrey type spaces on the unit disc”, Math. Notes, 100:1 (2016), 38–48 | DOI | MR | Zbl

[16] Karapetyants A., Samko S., “Mixed norm variable exponent Bergman space on the unit disc”, Complex Variables and Elliptic Equat., 61:8 (2016), 1090–1106 | DOI | MR | Zbl

[17] Karapetyants A., Smirnova I., “Weighted holomorphic mixed norm spaces in the unit disc defined in terms of Fourier coefficients”, Complex Variables and Elliptic Equat., 2021 | DOI

[18] Vasilevskii N. L., Grudskii S. M., Karapetyants A. N., “Dinamika svoistv teplitsevykh operatorov na vesovykh prostranstvakh Bergmana”, Sib. elektron. matem. izv., 3 (2006), 362–383 | MR | Zbl

[19] Grudsky S. M., Karapetyants A. N., Vasilevski N. L., “Toeplitz operators on the unit ball in $\mathbb{C}^n$ with radial symbols”, J. Operator Theory, 49:2 (2003), 325–346 | MR | Zbl

[20] Grudsky S. M., Karapetyants A. N., Vasilevski N. L., “Dynamics of properties of Toeplitz operators with radial symbols”, Integral Equat. Operator Theory, 50:2 (2004), 217–253 | DOI | MR | Zbl

[21] Grudsky S. M., Karapetyants A. N., Vasilevski N. L., “Dynamics of properties of Toeplitz operators on the upper half plane: hyperbolic case”, Bol. Soc. Mat. Mexicana (3), 10:1 (2004), 119–138 | MR | Zbl

[22] Grudsky S. M., Karapetyants A. N., Vasilevski N. L., “Dynamics of properties of Toeplitz operators on the upper half plane: parabolic case”, J. Operator Theory, 52:1 (2004), 185–214 | MR | Zbl

[23] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, ryadov i proizvedenii, 5-e izd., Fizmatgiz, M., 1971 | MR