Geodesic
New equivalent conditions for Hardy-type inequalities
Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 57-73.

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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.
DOI : 10.21136/MB.2023.0088-22
Classification : 26D10, 26D15, 47B01, 47B34, 47B37, 47B93, 47G10
Keywords: integral operator; norm; weight function; Lebesgue space; Hardy-type inequality; kernel 
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Kufner, Alois; Kuliev, Komil; Kulieva, Gulchehra; Eshimova, Mohlaroyim. New equivalent conditions for Hardy-type inequalities. Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 57-73. doi : 10.21136/MB.2023.0088-22. http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0088-22/

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