Boundedness and compactness of a certain class of matrix operators with variable limits of summation
Eurasian mathematical journal, Tome 11 (2020) no. 4, pp. 66-75.

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Necessary and sufficient conditions for the boundedness and compactness of the matrix operator of the form $(Af)_n=\sum_{k=\alpha(n)}^{\beta(n)}a_{n,k}f_k$, from $l_{p,v}$ to $l_{q,u}$ when $1$ are given.
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A. M. Temirkhanova; A. T. Beszhanova. Boundedness and compactness of a certain class of matrix operators with variable limits of summation. Eurasian mathematical journal, Tome 11 (2020) no. 4, pp. 66-75. http://geodesic.mathdoc.fr/item/EMJ_2020_11_4_a5/

[1] A. Alkhliel, “Discrete inequalities of Hardy type with variable limits of summation. I”, Bull. PFUR, 2010, no. 4, 56–69 (in Russian)

[2] A. Alkhliel, “Discrete inequalities of Hardy type with variable limits of summation. II”, Bull. PFUR, 2011, no. 1, 5–13 (in Russian)

[3] K. F. Andersen, H. P. Heinig, “Weighted norm inequalities for certain integral operators”, SIAM J. Math., 1983, no. 14, 834–844 | DOI | MR | Zbl

[4] E. N. Batuev, V. D. Stepanov, “Weighted inequalities of Hardy type”, Siberian Math. J., 30:1 (1989), 8–16 | DOI | MR | Zbl

[5] G. Bennet, “Some elementary inequalities III”, Quart. J. Math. Oxford Ser. (2), 42 (1991), 149–174 | DOI | MR | Zbl

[6] M. Sh. Braverman, V. D. Stepanov, “On the discrete Hardy inequality”, Bull. London Math. Soc., 26 (1994), 283–287 | DOI | MR | Zbl

[7] S. G. Krein (Ed.), Functional analysis, Wolters-Noordhoff Publishing, 1972 | MR | Zbl

[8] A. Kufner, L. Maligranda, L-E. Persson, The Hardy inequality. About its history and some related results, Vydavatelsky Servis Publishing House, Pilsen, 2007 | MR | Zbl

[9] R. Oinarov, “Boundedness and compactness of integral operators with variable integration limits in weighted Lebesgue spaces”, Siberian Math. J., 52:6 (2011), 1042–1055 | DOI | MR | Zbl

[10] R. Oinarov, S. Kh. Shalginbaeva, “Weighted additive estimate of a class of matrix operators”, Izvestiya NAN RK, ser. Phys. Mat., 2004, no. 1, 39–49 (in Russian) | MR

[11] R. Oinarov, L. E. Persson, A. Temirkhanova, “Weighted inequalities for a class of matrix operators: the case $p\leqslant q$”, Math. Inequal. Appl., 12:4 (2009), 891–903 | MR | Zbl

[12] D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Hardy-Steklov integral operators. I: II”, Proc. Steklov Inst. Math., 300:2 (2018), S1–S112 | MR | Zbl

[13] V. D. Stepanov, E. P. Ushakova, “On integral operators with variable limits of integration”, Proc. Steklov Inst. Math., 232 (2001), 290–309 | MR | Zbl

[14] V. D. Stepanov, E. P. Ushakova, “On the geometric mean operator with variable limits of integration”, Proc. Steklov Inst. Math., 260 (2008), 254–278 | DOI | MR | Zbl

[15] V. D. Stepanov, E. P. Ushakova, “Kernel operators with variable limits intervals of integration in Lebesgue spaces and applications”, Math. Inequal. Appl., 13 (2010), 449–510 | MR | Zbl

[16] Zh. Taspaganbetova, A. Temirkhanova, “Boundedness and compactness criteria of a certain class of matrix operators”, Math. Journal, 11:2 (40) (2011), 73–85 | MR