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What is the justification for this inequality?

  1. Dec 23, 2006 #1

    quasar987

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    What is the justification for this inequality?

    [tex]\int_0^1(|u(s)|+|v(s)|)(|u(s)|-|v(s)|)ds\leq \left(\int_0^1(|u(s)|^2+|v(s)|^2)ds\right)^{1/2}\left(\int_0^1(|u(s)-v(s)|^2)ds\right)^{1/2}[/tex]

    where u and v are complex-valued square-integrable Riemann integrable functions on [0,1].

    Thx.
     
  2. jcsd
  3. Dec 23, 2006 #2
    This reminds me of Holder's inequality, and the right hand side of the inequality is the L^2 norm. Go to Wikipedia and given p and q, your p and q equal 2.
     
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