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Title: A Hardy-Littlewood integral inequality on finite intervals with a concave weight
Authors: Alzer, H
Kwong, MK
Keywords: Concave weight function
Help-type inequality
Integral inequality
Issue Date: 2015
Publisher: Springer
Source: Periodica mathematica hungarica, 2015, v. 71, no. 2, p. 184-192 How to cite?
Journal: Periodica mathematica hungarica 
Abstract: We prove: For all concave functions w: [a, b] → [0, ∞) and for all functions f ε C2 [a,b] with f (a) = f (b) = 0 we have (∫a b w(x)f′ (x)2 dx) 2 ≤ (∫a b w(x) f(x)2dx) (∫a b w (x) f″(x)2 dx). Moreover, we determine all cases of equality.
ISSN: 0031-5303
DOI: 10.1007/s10998-015-0096-x
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