For any i would like to show the following:
I have done the following: To show an equality one can show that the case is true for both and . For the -case I have used the Cauchy-Schwarz inequality:
Now since we have that:
Taking the on both sides of the inequality yields:
If I could somehow get rid of the on the right side I would be home free. I could be tempted to reason that , but somehow that does not sound correct since .
Comments would be greatly appreciated.