ON THE BEST CONSTANT OF THE ONE-DIMENSIONAL BLISS INEQUALITY

摘要

In this article, we have established the domain invariance prop- erty of the best constant of the Bliss Inequality. In particular, we have proved that, for 1 < p < q < ∞ and 0 < b ≤ ∞, A_(p,q)(0, b) = B_(p,q)(0, b) = B_(p,q)~d (0, b) with r = q/p - 1. See Section 2. for notations. We also proved that the best constant is never achieved except for A_(p,q)(0, ∞) .