Journal of the
Korean Mathematical Society JKMS

In this paper, we establish the half-plane analogue of P. Ahern and \v{Z}. \v{C}u\v{c}kovi\'{c} (1996) characterization of almost subharmonicity of functions satisfying the inequality $\mathcal{B}f\geq f$, where $\mathcal{B}$ denotes the Berezin transform. As a byproduct, we investigate hyponormality of a class of Toeplitz operators with bounded harmonic symbols acting on the Bergman space of the complex upper half-plane.

Keywords: Hyponormanl operator, Berezin transform, Toeplitz operator

MSC numbers: 30A05