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    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.