Schatten class of Berezin transform on Fock spaces

Abstract

The Schatten norm for the nuclear operator $B_{\alpha}^{\ast}B_{\alpha}$ was estimated from both sides. Here $B_{\alpha}:L_{\beta}^{2}\rightarrow L_{\gamma}^{2}$ is the Berezin transform regarding the Fock spaces in the plane. Also, we found the norm  for the Berezin transform in case of unweighted Lebesgue spaces.