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It is a classical result that $L^p(\Omega) \subset L^q(\Omega)$ when $q<p$ and $|\Omega| < \infty$. I'd like to know if there is an Orlicz version of this fact. In other words, let $L^{G_1}$ and ...

I'm trying to check that certain examples of Young functions in the harmonic analysis literature are actually Young functions, and in doing so need to prove the following convexity-like inequality for ...