Invariant submean value inequality and hyponormality of Toeplitz operators on the upper half-plane
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In this paper, we establish the half-plane analogue of P. Ahern and \v{Z}. \v{C}u\v{c}kovi\'{c} \cite{AC1996} 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.\\
Abstract
In this paper, we establish the half-plane analogue of P. Ahern and \v{Z}. \v{C}u\v{c}kovi\'{c} \cite{AC1996} 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.\\