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On C LARKSON 's Inequalities and Interpolation
Author(s) -
Maligranda Lech,
Persson Lars Erik
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.19921550114
Subject(s) - mathematical proof , mathematics , interpolation (computer graphics) , class (philosophy) , inequality , elementary proof , point (geometry) , algebra over a field , pure mathematics , calculus (dental) , mathematical analysis , computer science , geometry , motion (physics) , medicine , dentistry , artificial intelligence
We consider some elementary proofs of local versions of C LARKSON 's inequalities and point out the fact that these inequalities can be generalized to hold for a much wider class of parameters. In particular it is easy to generalize our interpolation proof in various ways to higher dimensions. We point out explicitely some examples of such generalizations and we also prove some corresponding global versions. In this elementary way we obtain both new proofs of some previous results of this kind and also some new complements, unifications and further generalizations of these results.