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An Operation Connected to a Young-Type Inequality

✍ Scribed by Thomas Strömberg

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
630 KB
Volume
159
Category
Article
ISSN
0025-584X

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✦ Synopsis

Given two cp-functions F and G we consider the largest cp-function

Y o u m -t y p e inequality H(XY) F ( x ) + G(Y)

holds for all x, y > 0. We prove an equivalence theorem for F @ G with the best constants and, for the special case when F and G are log-convex and satisfy a certain growth condition, a representation formula for F @ G. Moreover, further properties and examples are presented and the relations to similar results are discussed.

*) The research reported here was supported in part by The Royal Swedish Academy of Sciences.

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