Far Eastern Mathematical Journal

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The estimates of the Schatten-Neumann norms of one class of integral operators

Lomakina E.N., Sarychev M.S.

2021, issue 2, P. 215–230 DOI: https://doi.org/10.47910/FEMJ202118

Abstract

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.

Keywords: Lebesque spaces, Lorentz spaces, integral operator, approximation numbers, Shatten-Neumann norms

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References

[1] A. Pich, Operatornye idealy, Mir, M., 1982. [2] I.Ts. Gokhberg, M.G. Krein, Vvedenie v teoriiu lineinykh nesamosopriazhennykh operatorov v gil'bertovom prostranstve, Nauka, M., 1965. [3] H. Konig, Eigenvalue distribution of compact operators. V. 16, Operator Theory: Advances and Applications, Birkhauser Verlag, Basel, 1986. [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, 2000, 153–187. [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. [6] E.N. Lomakina, “Ob otsenkakh norm operatora Khardi, deistvuiushchego v prostranstvakh Lorentsa”, Dal'nevostoch. matem. zhurn., 20:2 (2020), 191–211. [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. [9] E.T. Sawyer, “Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator”, Trans. Amer. Math. Soc., 281 (1984), 329–337. [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. [11] E.N. Lomakina, M.S. Sarychev, “Otsenki s-chisel integral'nogo operatora, deistvuiushchie iz prostranstv Lebega v prostranstva Lorentsa”, Informatsionnye tekhnologii i vysokoproizvoditel'nye vychisleniia. Materialy VI mezhdunarodnoi nauchno-prakticheskoi konferentsii, Khabarovsk, 14-16 sentiabria 2021, 55–63. [12] E.N. Lomakina, M.G. Nasyrova, V.V. Nasyrov, “O nekotorykh chislakh operatora Khardi v prostranstvakh Lorentsa”, Dal'nevostoch. matem. zhurn., 21:1 (2021), 56–78.

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