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On Hardy type inequalities in grand Lebesgue spaces Lp) for 0 < p ≤ 1
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2021-06-29 , DOI: 10.1080/03081087.2021.1944968
Rovshan A. Bandaliyev 1, 2 , Kamala H. Safarova 1
Affiliation  

In this paper, we prove the boundedness of Hardy operator for monotone functions in grand Lebesgue spaces Lp)(0, 1) (0 < p ≤ 1). In particular, we prove similar results for the Hardy operator in weighted Lebesgue spaces. Also, it is proved that the grand Lebesgue space Lp)(0, 1) is a quasi-Banach function space. Finally, we establish necessary and sufficient conditions for the boundedness of some integral operator in weighted quasi-Banach Lebesgue spaces.



中文翻译:

关于 0 < p ≤ 1 的大勒贝格空间 Lp) 的 Hardy 型不等式

在本文中,我们证明了大勒贝格空间L p ) (0, 1) (0 <  p  ≤ 1) 中单调函数的 Hardy 算子的有界性。特别是,我们在加权勒贝格空间中证明了 Hardy 算子的类似结果。并且证明了大勒贝格空间L p ) (0, 1)是一个拟Banach函数空间。最后,我们为加权拟 Banach Lebesgue 空间中的某个积分算子的有界性建立了充分必要条件。

更新日期:2021-06-29
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