Geodesic
On estimates for norms of some integral operators with Oinarov's kernel
Eurasian mathematical journal, Tome 13 (2022) no. 3, pp. 67-81.

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In this work, we give estimates for the norm of the integral operator \begin{equation} H: L_{p, v}\to L_{q, u}, \quad (Hf)(x):=\int_a^x k(x, t)f(t)dt \tag{0.1} \end{equation} with the so-called Oinarov's kernel $k(x, t)$ in the weighted Lebesgue spaces $$ L_{p, v}=\{f: ||f||_{p, v}^p:=\int_a^b |f(t)|^p v(t)dt\infty\} $$ and $$ L_{q, u}=\{f: ||f||_{q, u}^q:=\int_a^b |f(t)|^q u(t)dt\infty\}, $$ in the case $1$. 
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K. Kuliev. On estimates for norms of some integral operators with Oinarov's kernel. Eurasian mathematical journal, Tome 13 (2022) no. 3, pp. 67-81. http://geodesic.mathdoc.fr/item/EMJ_2022_13_3_a5/

[1] Kh. Almohammad, “On modular inequalities for generalized Hardy operators on weighted Orlicz spaces”, Eurasian Math. J., 12:3 (2021), 19–28 | DOI | MR | Zbl

[2] S. Bloom, R. Kerman, “Weighted norm inequalities for operators of Hardy type”, Proc. Amer. Math. Soc., 113:1 (1991), 135–141 | DOI | MR | Zbl

[3] A. Kalybay, A. Baiarystanov, “Exact estimate of norm of integral operator with Oinarov's condition”, Kazah. Math. J., 21 (2021), 6–14 | Zbl

[4] A. Kalybay, R. Oinarov, “Boundedness of Riemann-Liouville operator from weighted Sobolev space to weighted Lebesgue space”, Eurasian Math. J., 1:12 (2021), 39–48 | DOI | MR | Zbl

[5] A. Kufner, K. Kuliev, “Some characterizing conditions for the Hardy inequality”, Eurasian Math. J., 2:2 (2010), 86–98 | MR | Zbl

[6] A. Kufner, K. Kuliev, L.-E. Persson, “Some higher order Hardy inequalities”, Jour. Ineq Appl., 1:69 (2012), 1–14 | MR

[7] A. Kufner, L. Maligranda, L. E. Persson, The Hardy inequality-about its history and some related results, Pilsen, 2007 | MR | Zbl

[8] A. Kufner, L. E. Persson, Weighted inequalities of Hardy type, World scientific, New Jersey–London–Singapore–Hong Kong, 2003 | MR | Zbl

[9] F. J. Martin-Reyes, “Weights, one-sided operators, singular integrals and ergodic theorems”, Nonlinear Analysis, Function Spaces and Applications, v. 5, eds. M. Krbec, A. Kufner, B. Opic, J. Rakosnik, Prometheus, Prague, 1994, 103–137 | MR | Zbl

[10] F. J. Martin-Reyes, E. Sawyer, “Weighted inequalities for Riemann-Liouville fractional integrals of order one and greater”, Proc. Amer. Math. Soc., 3:106 (1989), 727–733 | DOI | MR | Zbl

[11] Soviet Math. Dokl., 44:1 (1992), 291–298 | MR | Zbl

[12] Proc. Steklov Inst. Math., 204:3 (1994), 205–214 | MR | Zbl

[13] L.-E. Persson, V. D. Stepanov, “Weighted integral inequalities with the geometric mean operator”, J. Inequal. Appl., 7:5 (2002), 727–746 | MR | Zbl

[14] M. A. Senouci, “Boundedness of Riemann-Liouville fractional integral operator in Morrey spaces”, Eurasian Math. J., 1:12 (2021), 82–91 | DOI | MR | Zbl

[15] V. D. Stepanov, “Weighted inequalities for a class of Volterra convolution operators”, J. London Math. Soc., 45:2 (1992), 232–242 | DOI | MR | Zbl

[16] A. M. Temirkhanova, A. T. Beszhanova, “Boundedness and compactness of a certain class of matrix operators with variable limits of summation”, Eurasian Math. J., 11:4 (2020), 66–75 | DOI | MR | Zbl