PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (211)
Orphanage
Unclass'd (1)
Unproven (472)
Corrections (36)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Very low Entry average rating: No information on entry rating
[parent] proof of Young Inequality (Proof)

By the concavity of the $ \log$ function we have

$\displaystyle \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.



"proof of Young Inequality" is owned by paolini.
(view preamble)

View style:


This object's parent.
Log in to rate this entry.
(view current ratings)

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 4831 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)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add example | add (any)