Geodesic
Boundedness of Toeplitz operators in weighted Sobolev spaces of functions holomorphic in the disk
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 257-282 
F. A. Shamoyan. Boundedness of Toeplitz operators in weighted Sobolev spaces of functions holomorphic in the disk. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 257-282. http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a14/
@article{ZNSL_2011_389_a14,
     author = {F. A. Shamoyan},
     title = {Boundedness of {Toeplitz} operators in weighted {Sobolev} spaces of functions holomorphic in the disk},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {257--282},
     year = {2011},
     volume = {389},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a14/}
}
TY  - JOUR
AU  - F. A. Shamoyan
TI  - Boundedness of Toeplitz operators in weighted Sobolev spaces of functions holomorphic in the disk
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 257
EP  - 282
VL  - 389
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a14/
LA  - ru
ID  - ZNSL_2011_389_a14
ER  - 
%0 Journal Article
%A F. A. Shamoyan
%T Boundedness of Toeplitz operators in weighted Sobolev spaces of functions holomorphic in the disk
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 257-282
%V 389
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a14/
%G ru
%F ZNSL_2011_389_a14

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A complete description is found for functions $h$ integrable on the unit circle and having the property that the Toeplitz operator whose symbol is $h$ is bounded in certain weighted Sobolev spaces of functions holomorphic in the disk.

[1] F. A. Shamoyan, “Ob ogranichennosti odnogo klassa operatorov, svyazannykh s delimostyu analiticheskikh funktsii”, Izv. AN ArmSSR. Ser. mat., 8:6 (1973), 474–490 | MR

[2] F. A. Shamoyan, “Ob odnom klasse operatorov, svyazannykh s faktorizatsiei analiticheskikh funktsii”, Zap. nauchn. semin. LOMI, 39, 1974, 200–205 | MR | Zbl

[3] F. A. Shamoyan, “Teplitsevy operatory i delenie na vnutrennyuyu funktsiyu v nekotorykh prostranstvakh analiticheskikh funktsii”, DAN ArmSSR, 76:3 (1983), 109–113 | MR | Zbl

[4] S. Janson, J. Peetre, A. Semmes, “On the action of Hankel and Toeplitz operators on some function spaces”, Duke Math. J., 51 (1984), 937–958 | DOI | MR | Zbl

[5] K. Zhu, “Multipliers of BMO in the Bergman metric with applications to Toeplitz operators”, J. Func. Anal., 87:1 (1989), 31–50 | DOI | MR | Zbl

[6] Songxiao Li, Stevo Stević, “Volterra type operators from Zygmund space into Bloch spaces”, J. Concr. Appl. Math., 6:2 (2008), 199–207 | MR | Zbl

[7] M. M. Dzhrbashyan, Integralnye preobrazovaniya i predstavlenie funktsii v kompleksnoi oblasti, Nauka, M., 1966 | Zbl

[8] F. A. Shamoyan, “Diagonalnye otobrazheniya i voprosy predstavleniya v anizotropnykh prostranstvakh golomorfnykh v polidiske funktsii”, Sibirskii mat. zh., 31:2 (1990), 197–215 | MR | Zbl

[9] O. E. Antonenkova, F. A. Shamoyan, “Preobrazovanie Koshi lineinykh nepreryvnykh funktsionalov i proektory v vesovykh prostranstvakh analiticheskikh funktsii”, Sibirskii mat. zh., 46:6 (2005), 1208–1234 | MR | Zbl

[10] N. M. Tkachenko, F. A. Shamoyan, “The Hardy–Littlewood theorem and the operator of harmonic conjugate in some classes of simply connected domains with rectifiable boundary”, J. Math. Physics, Analysis, Geometry, 5:2 (2009), 192–210 | MR | Zbl

[11] U. Rudin, Funktsionalnyi analiz, Mir, M., 1975 | MR