On Hardy type inequalities in grand Lebesgue spaces L _p) for 0 < p ≤ 1

In this paper, we prove the boundedness of Hardy operator for monotone functions in grand Lebesgue spaces (Formula presented.) In particular, we prove similar results for the Hardy operator in weighted Lebesgue spaces. Also, it is proved that the grand Lebesgue space (Formula presented.) 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.