Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space
The harmonic Bergman space \(L^2_{\mathrm{h}}\) is, by definition, the subspace of the space \(L^2\) with respect to area measure on the unit disc that consists of harmonic functions. Let \(Q\) be the orthogonal projection onto \(L^2_{\mathrm{h}}\). Given a bounded function \(\varphi\) on the unit disk, the Toeplitz operator \(T_\varphi\) and the Hankel operator \(H_\varphi\) are defined by \[ T_\varphi f=Q(\varphi f)\quad\text{and}\quad H_\varphi f=QU(\varphi f), \] where \((Uf)(z)=f(\bar z)\). The authors of the paper under review discuss algebraic properties of Toeplitz and Hankel operators.
scientific article; zbMATH DE number 6342510
scientific article