On Young's Inequality

Cunningham, Floyd F.; Grossman, Nathaniel

doi:10.1080/00029890.1971.11992852

Cited by 14 publications

(10 citation statements)

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“…(3 i (91 shows the validity of the left-hand side inequality in (7), since the infimum in the definition of F 0 G is attained. The right-hand side inequality in (7) follows from…”

Section: = Umentioning

confidence: 92%

“…More information about YOUNG'S *) The research reported here was supported in part by The Royal Swedish Academy of Sciences. 15' inequality in its classical form can be found in [3], [4], [5], [7], [9] and [lo]. YOUNG'S inequality has been generalized in several ways; see for instance PALES [16].…”

Section: P ( -I ) ( T ) =mentioning

confidence: 99%

“…Let us show that the constants 1 and 2 in the inequality (7) are the best possible. If F(x) = x, then, by Proposition 2, which is an example of equality in the right-hand side inequality of (7).…”

Section: Xcx(u)mentioning

confidence: 99%

“…and Thus, Hence, the number 1 in the left-hand side inequality in (7) cannot be replaced by any larger number.…”

Section: Xcx(u)mentioning

confidence: 99%

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An Operation Connected to a Young‐Type Inequality

Strömberg¹

1992

Mathematische Nachrichten

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Given two cp-functions F and G we consider the largest cp-function H = F 0 G such that the 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.

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“…(3 i (91 shows the validity of the left-hand side inequality in (7), since the infimum in the definition of F 0 G is attained. The right-hand side inequality in (7) follows from…”

Section: = Umentioning

confidence: 92%

Section: P ( -I ) ( T ) =mentioning

confidence: 99%

Section: Xcx(u)mentioning

confidence: 99%

“…and Thus, Hence, the number 1 in the left-hand side inequality in (7) cannot be replaced by any larger number.…”

Section: Xcx(u)mentioning

confidence: 99%

See 2 more Smart Citations

An Operation Connected to a Young‐Type Inequality

Strömberg¹

1992

Mathematische Nachrichten

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“…Remark 1. (F. Cunningham Jr. and N. Grossman [2]). Since pseudo-inverses will be used as integrands, it is convenient to enlarge the concept of pseudo-inverse by referring to any function g such that…”

Section: Young's Inequality For Weighted Measuresmentioning

confidence: 99%