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An Operation Connected to a Young‐Type Inequality
Author(s) -
Strömberg Thomas
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921590116
Subject(s) - mathematics , equivalence (formal languages) , type (biology) , regular polygon , convex function , inequality , function (biology) , pure mathematics , combinatorics , representation (politics) , discrete mathematics , mathematical analysis , geometry , ecology , evolutionary biology , politics , law , biology , political science
Given two φ‐functions F and G we consider the largest φ‐function H = F ⊕ G such that the Young‐ type 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.