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proof of Young Inequality
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(Proof)
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By the concavity of the $\log$ function we have $$ \log ab = \frac 1 p \log a^p + \frac 1 q \log b^q \le \log(\frac 1 p a^p + \frac 1 q b^q). $$ By exponentiation we obtain the desired result.
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"proof of Young Inequality" is owned by paolini.
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Cross-references: function
This is version 1 of proof of Young Inequality, born on 2003-03-07.
Object id is 4079, canonical name is ProofOfYoungInequality.
Accessed 6488 times total.
Classification:
| AMS MSC: | 46E30 (Functional analysis :: Linear function spaces and their duals :: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant) |
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Pending Errata and Addenda
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