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On Some Sharp Reversed Hölder and Hardy Type Inequalities
Author(s) -
Bergh Jöran,
Burenkov Victor,
Persson Lars Erik
Publication year - 1994
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.19941690103
Subject(s) - mathematics , monotonic function , monotone polygon , inequality , type (biology) , pure mathematics , mathematical analysis , mathematical economics , calculus (dental) , geometry , medicine , ecology , dentistry , biology
We discuss some reversed Hölder inequalities yielding for functions on R + satisfying one or two conditions of quasi‐monotonicity. All cases of equality are pointed out. By using these results and some recent results by the present authors (see [3]), we prove some new reversed inequalities of Hardy type for quasi‐monotone functions. In some cases we obtain the best constants and all cases of equality are obtained. Some applications, open questions and the relations to other similar results are pointed out.