The estimates of the Schatten--Neumann norms of one class of integral operators
Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 215-230.

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

The article considers an integral operator acting from Lebesque spaces to Lorentz spaces. The conditions are found under which the compact operator belongs to the Shatten–Neumann classes.
@article{DVMG_2021_21_2_a7,
     author = {E. N. Lomakina and M. S. Sarychev},
     title = {The estimates of the {Schatten--Neumann} norms of one class of integral operators},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {215--230},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a7/}
}
TY  - JOUR
AU  - E. N. Lomakina
AU  - M. S. Sarychev
TI  - The estimates of the Schatten--Neumann norms of one class of integral operators
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2021
SP  - 215
EP  - 230
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a7/
LA  - ru
ID  - DVMG_2021_21_2_a7
ER  - 
%0 Journal Article
%A E. N. Lomakina
%A M. S. Sarychev
%T The estimates of the Schatten--Neumann norms of one class of integral operators
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2021
%P 215-230
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a7/
%G ru
%F DVMG_2021_21_2_a7
E. N. Lomakina; M. S. Sarychev. The estimates of the Schatten--Neumann norms of one class of integral operators. Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 215-230. http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a7/

[1] A. Pich, Operatornye idealy, Mir, M., 1982

[2] I. Ts. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965

[3] H. König, Eigenvalue distribution of compact operators, v. 16, Operator Theory: Advances and Applications, Birkhäuser Verlag, Basel, 1986 | DOI

[4] E. Lomakina, V. Stepanov, “On asymptotic behaviour of the approximation numbers and estimates of Schatten von Neumann norms of the Hardy–type integral operators”, Function spaces and application, Narosa Publishing Hause, New Delhi, 2000, 153–187 | Zbl

[5] E. Lomakina, V. Stepanov, “On the compactness and approximation numbers of Hardy type integral operators in Lorentz spases”, J. London Math. Soc. (2), 53 (1996), 369–382 | DOI | MR | Zbl

[6] E. N. Lomakina, “Ob otsenkakh norm operatora Khardi, deistvuyuschego v prostranstvakh Lorentsa”, Dalnevostoch. matem. zhurn., 20:2 (2020), 191–211 | MR | Zbl

[7] C. Bennett, R. Sharpley, Interpolation of Operators, v. 129, Pure and Applied Mathematics, Academic Press, Boston, 1988

[8] S. Barza, V. Kolyada V., J. Soria, “Sharp constants related to the triangle inequality in Lorentz spaces”, Trans. Amer. Math. Soc., 361:10 (2009), 5555–5574 | DOI | MR | Zbl

[9] E. T. Sawyer, “Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator”, Trans. Amer. Math. Soc., 281 (1984), 329–337 | DOI | MR | Zbl

[10] D. E. Edmunds, P. Gurka, L. Pick, “Compactness of Hardy-type integral operators in weighted Banach function spaces”, Studia Math., 109 (1994), 73–90 | MR | Zbl

[11] E. N. Lomakina, M. S. Sarychev, “Otsenki s-chisel integralnogo operatora, deistvuyuschie iz prostranstv Lebega v prostranstva Lorentsa”, Informatsionnye tekhnologii i vysokoproizvoditelnye vychisleniya, Materialy VI mezhdunarodnoi nauchno-prakticheskoi konferentsii (Khabarovsk, 14-16 sentyabrya 2021), 2021, 55–63

[12] E. N. Lomakina, M. G. Nasyrova, V. V. Nasyrov, “O nekotorykh chislakh operatora Khardi v prostranstvakh Lorentsa”, Dalnevostoch. matem. zhurn., 21:1 (2021), 56–78 | MR