A mixed-norm version of Minkowski’s integral inequality is proved in detail, and combined with the mixed-norm Hölder’s inequality to produce new, more general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to follow as special cases. Examples show how other estimates can be easily proved using these mixed-norm inequalities. Finally, the effectiveness of this technique is demonstrated by deriving a new inequality, combining features from two previous results.
Positivity – Springer Journals
Published: May 18, 2016
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