Norm of the Hilbert matrix operator on the weighted Bergman spaces

Abstract

We find the lower bound for the norm of the Hilbert matrix operator H on the weighted Bergman space A^p,α ||H||A^p,α→ A^p,α≥ π/sin(α+2)π/p for lt;α+2 < p. We show that if 4 ≤ 2(α + 2) ≤ p, then ||H||A^p,α → A^p,α = , while if 2 ≤ α +2 < p < 2(α+2), upper bound for the norm ||H||A^p,α → A^p,α, better then known, is obtained.