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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.

##### MSC:
 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.)
##### Keywords:
variable Lebesgue space; weight; Hardy operator; boundedness
Full Text:
##### References:
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