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The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces. (English) Zbl 1222.47045
Czech. Math. J. 60, No. 2, 327-337 (2010); corrigendum ibid. 63, No. 4, 1149-1152 (2013).
Summary: The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application, we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space.

47B38 Linear operators on function spaces (general)
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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