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Homework Help: Bounding p-norm expression

  1. Dec 3, 2017 #1
    problem statement:

    need to show:
    [tex]||w||_p^2+||u||_p^2-2(||u||_p^p)^{\frac{2}{p}-1}\Sigma_i(u(i)^{p-1}w(i)) [/tex]

    can be bounded as a function of

    [tex] ||w-u||_p^2 [/tex]

    where [tex] p\in[2,\infty) [/tex]

    work done:

    the expressions are equal for p=2, and i suspect that

    [tex] ||w||_p^2+||u||_p^2-2(||u||_p^p)^{\frac{2}{p}-1}\Sigma_i(u(i)^{p-1}w(i)) \leq||w-u||_p^2 [/tex]

    but i get stuck here. Is there some kind of p-norm inequality I can apply here?


    Thank you!
     
  2. jcsd
  3. Dec 3, 2017 #2

    StoneTemplePython

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    Science Advisor
    Gold Member

    Forum rules require you to show your work. From what I see, you just took the problem statement and re-wrote it with "I suspect that" it holds as an upper bound with a scalar multiple of one.

    What kind of work can you show to at least justify your suspicion?
     
    Last edited: Dec 3, 2017
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