Received June 23, 2022. Published online March 3, 2023.
Abstract: We consider a Hardy-type inequality with Oinarov's kernel in weighted Lebesgue spaces. We give new equivalent conditions for satisfying the inequality, and provide lower and upper estimates for its best constant. The findings are crucial in the study of oscillation and non-oscillation properties of differential equation solutions, as well as spectral properties.
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Affiliations: Alois Kufner, Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567 Praha 1, Czech Republic, e-mail: kufner@math.cas.cz; Komil Kuliev (corresponding author), Uzbek-Finnish Pedagogical Institute of Samarkand State University, Samarkand 140104, Uzbekistan and Institute of Mathematics named after V. I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan, Tashkent 100174, Uzbekistan, e-mail: komilkuliev@gmail.com; Gulchehra Kulieva, Samarkand State University, Samarkand 140104, Uzbekistan, e-mail: gkulieva@mail.ru; Mohlaroyim Eshimova, Institute of Mathematics named after V. I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan, Tashkent 100174, Uzbekistan, e-mail: eshimova_math@mail.ru
