Generalized Hilbert operators on Bergman and Dirichlet spaces of analytic functions (Q2787107)

The generalized Hilbert operator \({\mathcal H}_{a,b}\) is defined by NEWLINE\[NEWLINE ({\mathcal H}_{a,b}f)(z)=\frac{\Gamma(a+1)}{\Gamma(b+1)}\int_0^1\frac{f(t)(1-t)^b}{(1-tz)^{a+1}}dt, NEWLINE\]NEWLINE where \(f\) is an analytic function in the unit disk. The authors of the article under review find conditions on \(a\) and \(b\), under which \({\mathcal H}_{a,b}\) is a bounded operator on Dirichlet-type spaces and on Bergman spaces.