Trace class criteria for Toeplitz and composition operators on small Bergman spaces (Q261195)

For \(0<p<\infty\), let \(A^p_{\omega}\) denote the weighted Bergman space on the unit disk induced by a radial weight \(\omega\) satisfying the doubling property \(\int_r^1 \omega(s)\,ds\leq C\int_{\frac{1+r}{2}}^1 \omega(s)\, ds\).NEWLINENEWLINEAs their main result, the authors characterize the Schatten class Toeplitz operators defined on \(A^p_{\omega}\) and Schatten class composition operators with analytic symbols acting between two weighted Bergman spaces. Additionally, the authors give some conditions for composition operators from \(A^p_{\omega}\) to \(A^p_{\nu}\), where \(\omega\) and \(\nu\) are radial, and \(\omega\) satisfies the doubling property, to be bounded and compact.