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New equivalent conditions for Hardy-type inequalities

Alois Kufner, Komil Kuliev, Gulchehra Kulieva, Mohlaroyim Eshimova (2024)

Mathematica Bohemica

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.

Nonlinear operators of integral type in some function spaces.

Carlo Bardaro, Gianluca Vinti, J. Musielak (1997)

Collectanea Mathematica

We give results about embeddings, approximation and convergence theorems for a class of general nonlinear operators of integral type in abstract modular function spaces. Thus we extend some previous result on the matter.

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