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arXiv · 2407.20115

Weighted inequalities for sub-monotone functionals

Amiran Gogatishvili·Luboš Pick
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Abstract

We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve a specific problem by transferring it to another one for which a solution is known. The main result is formulated in a rather surprising generality, involving previously unknown cases, and it works even for some nonlinear operators such as the geometric or harmonic mean operators. Proofs use only elementary means.

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Amiran Gogatishvili, Luboš Pick. 2024-07-29. Weighted inequalities for sub-monotone functionals. https://arxiv.org/abs/2407.20115

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