Abstract
We study products of Toeplitz operators with angular symbols on the Bergman space over the upper half-plane. We establish necessary and sufficient conditions for the product of two such Toeplitz operators to give rise to a Toeplitz operator, especially in case one of the symbols is absolutely continuous or with bounded variation. Our conditions make appeal to Volterra and Fredholm integral equations, and to Duhamel–Mikusiński convolution products as well as to functional equations involving Stieltjes integrals. We illustrate our results by concrete examples showing that there are many angular symbols satisfying our natural conditions and ensuring Toeplitzness of such Toeplitz products.