On Hardy type inequalities in grand Lebesgue spacesLp)for 0 <p≤ 1

2021/06/29 by Rovshan A. Bandaliyev, Kamala H. Safarova, K. H. Safarova
Mathematics · Social Sciences · #Advanced Harmonic Analysis Research #Advanced Banach Space Theory #Polish Legal and Social Issues

paper · doi:10.1080/03081087.2021.1944968

Abstract

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.

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