What is the justification for this inequality?

  • Thread starter quasar987
  • Start date

quasar987

Science Advisor
Homework Helper
Gold Member
4,771
7
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.
 
62
0
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.
 

Related Threads for: What is the justification for this inequality?

  • Last Post
Replies
4
Views
788
  • Last Post
Replies
6
Views
2K
Replies
5
Views
871
  • Last Post
Replies
3
Views
1K
Replies
19
Views
876
Replies
1
Views
1K
Replies
4
Views
528

Hot Threads

Top