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Keywords:
variable Lebesgue space; weight; sublinear operator; boundedness
variable Lebesgue space; weight; sublinear operator; boundedness
Summary:
In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an application he proved the boundedness of certain sublinear operators on the weighted variable Lebesgue space. The proof of the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent does not contain any mistakes. But in the proof of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in my paper, which was published as R. A. Bandaliev, The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces, Czech. Math. J. 60 (2010), 327–337.
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References:
[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
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