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On the Best Constant in Weighted Inequalities for Riemann‐Liouville Integrals
Author(s) -
Manakov Viktor M.
Publication year - 1992
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/24.5.442
Subject(s) - mathematics , constant (computer programming) , riemann hypothesis , combinatorics , mathematical physics , mathematical analysis , pure mathematics , computer science , programming language
For 1 ⩽ k < ∞ and 1 ⩽ p ⩽ q ∞, the problem of finding the best constant C p q in the weighted inequality( ∫ 0 ∞|I k f ( x )| q| u ( x )| q d x )1 / q ⩽ C p , q( ∫ 0 ∞| f ( x )| p| υ ( x )| p d x )1 / p , involving the Riemann‐Liouville integrals of the formI k f ( x ) = 1 Γ ( k )∫ 0 x( x ‐ t )k ‐ 1 f ( t ) d t , is considered.
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