We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We give some new characterizations for compactness of weighted composition operators 
$u{{C}_{\varphi }}$ acting on Bloch-type spaces in terms of the power of the components of 
$\varphi$, where $\varphi$ is a holomorphic self-map of the polydisk 
${{\mathbb{D}}^{n}}$, thus generalizing the results obtained by Hyvärinen and Lindström in 2012.
We consider the problem of determining for which square integrable functions 
$f$ and 
$g$ on the polydisk the densely defined Hankel product 
${{H}_{f}}\,H_{g}^{*}$ is bounded on the Bergman space of the polydisk. Furthermore, we obtain similar results for the mixed Haplitz products 
${{H}_{g}}\,{{T}_{{\bar{f}}}}$ and 
${{T}_{f}}\,H_{g}^{*}$, where $f$ and $g$ are square integrable on the polydisk and $f$ is analytic.
