# Young's functional with Lebesgue-Stieltjes integrals

@article{Merkle2011YoungsFW, title={Young's functional with Lebesgue-Stieltjes integrals}, author={Milan Merkle and Dan Ştefan Marinescu and Monica Moulin Ribeiro Merkle and Mihai Monea and Marian Stroe}, journal={arXiv: Classical Analysis and ODEs}, year={2011} }

For non-decreasing real functions $f$ and $g$, we consider the functional $ T(f,g ; I,J)=\int_{I} f(x)\di g(x) + \int_J g(x)\di f(x)$, where $I$ and $J$ are intervals with $J\subseteq I$. In particular case with $I=[a,t]$, $J=[a,s]$, $s\leq t$ and $g(x)=x$, this reduces to the expression in classical Young's inequality. We survey some properties of Lebesgue-Stieltjes interals and present a new simple proof for change of variables. Further, we formulate a version of Young's inequality with…

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