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variable Lebesgue space; weight; sublinear operator; boundedness

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[1] Bandaliev, R. A.: **The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces**. Czech. Math. J. 60 (2010), 327-337. DOI 10.1007/s10587-010-0038-y | MR 2657952 | Zbl 1222.47045

[2] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: **Lebesgue and Sobolev Spaces with Variable Exponents**. Lecture Notes in Mathematics 2017 Springer, Berlin (2011). MR 2790542 | Zbl 1222.46002