H-Toeplitz operators on the Dirichlet type space

In this paper, we conducted a study of H-Toeplitz operators on the Dirichlet type space ${\mathfrak{D}}_t$, which included several aspects. To begin, we established the matrix representation of the H-Toeplitz operator $S_{\phi }$ with respect to the orthonormal basis of ${\mathfrak{D}}_t$. Subsequently, we characterized the compactness of $S_{\phi }$ in terms of the symbol $\phi$. Furthermore, we developed a new method to investigate the algebraic properties of H-Toeplitz operators, including self-adjointness, diagonality, co-isometry, partial isometry as well as commutativity.