  The mixed-norm versions of the H\"older 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 H\"older 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.
