Maximal operator on variable Lebesgue spaces for almost monotone radial exponent |
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Authors: | Ale&scaron Nekvinda |
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Affiliation: | Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 16629 Prague 6, Czech Republic |
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Abstract: | We study general Lebesgue spaces with variable exponent p. It is known that the classes L and N of functions p are such that the Hardy-Littlewood maximal operator is bounded on them provided p∈L∩P. The class L governs local properties of p and N governs the behavior of p at infinity.In this paper we focus on the properties of p near infinity. We extend the class N to a collection D of functions p such that the Hardy-Littlewood maximal operator is bounded on the corresponding variable Lebesgue spaces provided p∈L∩D and the class D is essentially larger than N.Moreover, the condition p∈D is quite easily verifiable in the practice. |
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Keywords: | Maximal operator Lebesgue spaces Variable exponent Radial function |
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