Question: Let w(x) > 0 for a (a) Prove that defines a norm on C°[«. h ]. called the weighted L1 norm. (b) Do the same

Let w(x) > 0 for a (a) Prove that
Ifli = If (x)| w(x) dx %3D

defines a norm on C°[«. h ]. called the weighted L1 norm.
(b) Do the same for the weighted Lˆž norm
||f||ˆž.u, = max{|f(x)| w(x) ; a ‰¤ x ‰¤ h }.

Ifli = If (x)| w(x) dx %3D

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