Weighted inequalities for sub-monotone functionals
Classical Analysis and ODEs
2025-03-13 v2 Analysis of PDEs
Functional Analysis
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.
Cite
@article{arxiv.2407.20115,
title = {Weighted inequalities for sub-monotone functionals},
author = {Amiran Gogatishvili and Luboš Pick},
journal= {arXiv preprint arXiv:2407.20115},
year = {2025}
}