Mixed-norm estimates and symmetric geometric means

Mixed-norm estimates and symmetric geometric means 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Mixed-norm estimates and symmetric geometric means

Positivity , Volume 21 (1) – May 18, 2016
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Publisher
Springer International Publishing
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-016-0424-2
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

PositivitySpringer Journals

Published: May 18, 2016

References

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