# Riesz Representation Theorem and Hoelder's Inequality

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On Problems 4 and 5 with 1<p< infinity and q the index dual to p, it will be

helpful to remember from the proof of Young's inequality

that, for y and z positive numbers,

y^p = z^q if and only if

y=z^(q-1) if and only if

z=y^(p-1) and, under these equivalent conditions,

zy = y^p =z^q.

See attached file for full problem description.

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#### Solution Summary

The Riesz Representation Theorem and Hoelder's Inequality are investigated.

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