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Inequalities for Indefinite Forms

✍ Scribed by László Losonczi; Zsolt Páles

Book ID
102592290
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
125 KB
Volume
205
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

1, . . . , n , x G x q иии qx if p ) 0 and x ) 0 i s 1, . . . , n , x ) x q иии qx

Three inequalities are presented for ⌽ . The first is a comparison theorem. The p Ž second is a ''Holder-like'' generalization of Aczel's inequality an extension of ¨.

Popoviciu's inequality , while the third is a generalization of Bellman's inequality to all possible values of p. The proofs show that the above inequalities are consequences of some well-known inequalities for power means and power sums.

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This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder i