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AdvancesinAppliedMathematicsA^êÆ?Ð,2023,12(3),1068-1076
PublishedOnlineMarch2023inHans.https://www.hanspub.org/journal/aam
https://doi.org/10.12677/aam.2023.123108
ŒÈ¼êH¨olderØªdØª
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H¨olderØª§Žâ²þ-AÛ²þØª§˜²þØª§d5
EquivalentInequalitiesoftheH¨older
InequalityforIntegrableFunctions
ShiyuShen,ShengjieZhang,WenbinZhang
SchoolofMathematicsandStatistics,ChangshuInstituteofTechnology,ChangshuJiangsu
Received:Feb.15
th
,2023;accepted:Mar.11
th
,2023;published:Mar.20
th
,2023
Abstract
H¨olderinequalityplaysanextremelyimportantroleinanalysisandelementaryin-
equalitytheory.Asanimportantaspectofrelatedresearch,thestudyofitsequiva-
©ÙÚ^:!˜…,Ü•q,Ü©Q.ŒÈ¼êH¨olderØªdØª[J].A^êÆ?Ð,2023,12(3):1068-1076.
DOI:10.12677/aam.2023.123108
!˜…
lencerelationshipwithotherinequalitieshasalsoreceivedincreasingattention.This
paperprovestheH¨olderinequalityandtheAM-GMinequalityinmeasurespace,and
itsequivalencerelationshipwiththepowermeaninequality.Theseresultsgeneralize
thediscreteinequalityequivalencerelationshiprecentlyestablishedbyLietal.
Keywords
H¨olderInequality,AM-GMInequality,PowerAverageInequality,Equivalence
Copyright
c
2023byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution InternationalLicense(CCBY4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/aam.2023.1231081069A^êÆ?Ð
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DOI:10.12677/aam.2023.1231081070A^êÆ?Ð
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DOI:10.12677/aam.2023.1231081071A^êÆ?Ð
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DOI:10.12677/aam.2023.1231081072A^êÆ?Ð
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DOI:10.12677/aam.2023.1231081073A^êÆ?Ð
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