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On the Best Constant in Weighted Inequalities for Riemann‐Liouville Integrals

On the Best Constant in Weighted Inequalities for Riemann‐Liouville Integrals For 1 ⩽ k < ∞ and 1 ⩽ p ⩽ q ∞, the problem of finding the best constant Cpq in the weighted inequality (∫0∞| Ikf(x) |q| u(x) |qdx)1/q⩽Cp,q(∫0∞| f(x) |p| υ(x) |pdx)1/p, involving the Riemann‐Liouville integrals of the form Ikf(x)=1Γ(k)∫0x(x‐t)k‐1f(t)dt, is considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

On the Best Constant in Weighted Inequalities for Riemann‐Liouville Integrals

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/24.5.442
Publisher site
See Article on Publisher Site

Abstract

For 1 ⩽ k < ∞ and 1 ⩽ p ⩽ q ∞, the problem of finding the best constant Cpq in the weighted inequality (∫0∞| Ikf(x) |q| u(x) |qdx)1/q⩽Cp,q(∫0∞| f(x) |p| υ(x) |pdx)1/p, involving the Riemann‐Liouville integrals of the form Ikf(x)=1Γ(k)∫0x(x‐t)k‐1f(t)dt, is considered.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Sep 1, 1992

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