no. 1
Schatten properties of Toeplitz operators on the Paley–Wiener space
[Propriétés des opérateurs de Toeplitz de classes de Schatten sur l’espace de Paley-Wiener]
Bessonov, R. V.1
1 St. Petersburg State University 29b, 14th Line V.O., 199178, St. Petersburg (Russia) and St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Science 27, Fontanka, 191023, St. Petersburg (Russia)
Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 195-215.

Nous présentons plusieurs descriptions anciennes et nouvelles des opérateurs de Toeplitz de classe de Schatten sur l’espace de Paley-Wiener et répondons à une question de Richard Rochberg sur les commutateurs discrets de la transformée de Hilbert.

We collect several old and new descriptions of Schatten class Toeplitz operators on the Paley–Wiener space and answer a question on discrete Hilbert transform commutators posed by Richard Rochberg.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3157
Classification : 47B35, 46E39
Keywords: Paley–Wiener space, Schatten ideal, discrete Besov space, discrete Hilbert transform commutator
Mot clés : Espace de Paley–Wiener space, Idéal de Schatten, Espace de Besov discret

Bessonov, R. V. 1

1 St. Petersburg State University 29b, 14th Line V.O., 199178, St. Petersburg (Russia) and St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Science 27, Fontanka, 191023, St. Petersburg (Russia)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{AIF_2018__68_1_195_0,
     author = {Bessonov, R.~V.},
     title = {Schatten properties of {Toeplitz} operators on the {Paley{\textendash}Wiener} space},
     journal = {Annales de l'Institut Fourier},
     pages = {195--215},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {68},
     number = {1},
     year = {2018},
     doi = {10.5802/aif.3157},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3157/}
}
TY  - JOUR
AU  - Bessonov, R. V.
TI  - Schatten properties of Toeplitz operators on the Paley–Wiener space
JO  - Annales de l'Institut Fourier
PY  - 2018
SP  - 195
EP  - 215
VL  - 68
IS  - 1
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.3157/
DO  - 10.5802/aif.3157
LA  - en
ID  - AIF_2018__68_1_195_0
ER  - 
%0 Journal Article
%A Bessonov, R. V.
%T Schatten properties of Toeplitz operators on the Paley–Wiener space
%J Annales de l'Institut Fourier
%D 2018
%P 195-215
%V 68
%N 1
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.3157/
%R 10.5802/aif.3157
%G en
%F AIF_2018__68_1_195_0
Bessonov, R. V. Schatten properties of Toeplitz operators on the Paley–Wiener space. Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 195-215. doi : 10.5802/aif.3157. https://aif.centre-mersenne.org/articles/10.5802/aif.3157/

[1] Bessonov, Roman V. Fredholmness and compactness of truncated Toeplitz and Hankel operators, Integral Equations Oper. Theory, Volume 82 (2015) no. 4, pp. 451-467 | DOI | Zbl

[2] Levin, Boris Ya. Lectures on entire functions, Translations of Mathematical Monographs, 150, American Mathematical Society, 1996 | Zbl

[3] Lopatto, Patrick; Rochberg, Richard Schatten-class truncated Toeplitz operators, Proc. Am. Math. Soc., Volume 144 (2016) no. 2, pp. 637-649 | DOI | Zbl

[4] Peetre, Jaak New thoughts on Besov spaces, Duke University Mathematics Series, 1, Mathematics Department, Duke University, 1976 | Zbl

[5] Peller, Vladimir V. Wiener–Hopf operators on a finite interval and Schatten–von Neumann classes, Proc. Am. Math. Soc., Volume 104 (1988) no. 2, pp. 479-486 | DOI | Zbl

[6] Peller, Vladimir V. Hankel operators and their applications, Springer Monographs in Mathematics, Springer, 2003, xvi+784 pages | MR | Zbl

[7] Plancherel, Michel; Pólya, George Fonctions entières et intégrales de Fourier multiples, Comment. Math. Helv., Volume 10 (1937) no. 1, pp. 110-163 | DOI | Zbl

[8] Rochberg, Richard Decomposition theorems for Bergman spaces and their applications, Operators and function theory (NATO ASI Series. Series C: Mathematical and Physical Sciences), Volume 153, D. Reidel Publishing Company, 1985, pp. 225-277 | Zbl

[9] Rochberg, Richard Toeplitz and Hankel operators on the Paley–Wiener space, Integral Equations Oper. Theory, Volume 10 (1987) no. 2, pp. 187-235 | DOI | MR | Zbl

[10] Smith, Martin The reproducing kernel thesis for Toeplitz operators on the Paley–Wiener space, Integral Equations Oper. Theory, Volume 49 (2004) no. 1, pp. 111-122 | DOI | Zbl

[11] Torres, Rodolfo H. Spaces of sequences, sampling theorem, and functions of exponential type, Studia Mathematica, Volume 100 (1991) no. 1, pp. 51-74 | DOI | Zbl

[12] Torres, Rodolfo H. Mean oscillation of functions and the Paley-Wiener space, J. Fourier Anal. Appl., Volume 4 (1998) no. 3, pp. 283-297 | DOI | Zbl

Cité par Sources :