Mixed-norm estimates and symmetric geometric means

The mixed-norm versions of the Hölder and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special cases of these new results. Examples are also given of applying mixed-norm Hölder and Minkowski to other estimates, providing much easier proofs. Finally, the effectiveness of this technique is demonstrated by deriving a new inequality which combines features from two separate previous results.

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