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On a Class of Integral Inequalities
Author(s) -
Everitt W. N.,
Zettl A.
Publication year - 1978
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-17.2.291
Subject(s) - class (philosophy) , inequality , mathematics , calculus (dental) , pure mathematics , mathematical analysis , computer science , artificial intelligence , medicine , dentistry
The Titchmarsh‐Weyl coefficient for the differential equation −( x β y ′ ( x ) ) ′ = λ x α y ( x ) ( x ∈ ( 0 , ∞ ) )where the real parameters α and β satisfy α = − 1 and β < 1, is calculated explicitly. The result is applied to obtain the best possible constant K(α,β) in the integral inequality(∫ 0 ∞x β f ′( x ) 2 d x) ⩽ K ( α , β )∫ 0 ∞x α f ( x )2 d x∫ 0 ∞x − α{( x β f ′ ( x ) ) ′ } 2 d x .