I have been set the following question.
Show that the operator L[f](x) = INT(0,x) f(s) dx , 0<= x <=1 , is bounded from C0(0,1) into itself.
where INT(0,x) is the integral between 0 and x, and C0(0,1) is the space of continuous functions with no continuous derivatives on (0,1).
I know that to show this I must show there exists c>0 such that
llLxll <= cllxll for all x.
However I am having trouble actually showing this exists. any ideas?