On the Best Constant in Weighted Inequalities for Riemann‐Liouville Integrals
On the Best Constant in Weighted Inequalities for Riemann‐Liouville Integrals
Manakov, Viktor M.
1992-09-01 00:00:00
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.pngBulletin of the London Mathematical SocietyWileyhttp://www.deepdyve.com/lp/wiley/on-the-best-constant-in-weighted-inequalities-for-riemann-liouville-zUSA5ed0lZ
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.
Journal
Bulletin of the London Mathematical Society
– Wiley
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