ON THE BEST CONSTANT IN WEIGHTED INEQUALITIES FOR RIEMANN-LIOUVILLE INTEGRALS

For 1 less-than-or-equal-to k < infinity and 1 < p less-than-or-equal-to q < infinity, the problem of finding the best constant C(p,q) in the weighted inequality (integral-infinity/0 \I(k)f(x)\q\u(x)\q dx)1/q less-than-or-equal-to C(p,q)(integral-infinity/0 \f(x)\p\v(x)\p dx)1/p, involving the Riemann-Liouville integrals of the form I(k)f(x) = 1/GAMMA(k) integral-x/0 (x-1)k-1f(t)dt, is considered.