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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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Sort-of extension of Young inequality to arbitrary measures
The most general version of Young's convolution inequality that I know of is as follows: Let $(X,\mu)$ be a $\sigma$-finite measure space. For $1 \leq p, r \leq \infty$,
$\left\|f \ast g\right\|_{L^ …