Norm of the Hilbert matrix on Bergman spaces

Abstract

It is well known that the Hilbert matrix operator H is a bounded operator from the Bergman space Ap into Ap if and only if 2<p<∞. In [5] it was shown that the norm of the Hilbert matrix operator H on the Bergman space Ap is equal to [Formula presented], when 4≤p<∞, and it was also conjectured that ‖H‖Ap→Ap=[Formula presented], when 2<p<4. In this paper we prove this conjecture.