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.
Funding statement: The authors would like to thank the Deanship of Scientific Research of King Saud University for funding and supporting this research through the initiative of DSR Graduate Students Research Support (GSR).
Acknowledgements
The authors would like to thank Professor Roland Duduchava and Professor Nikolai Vasilevski for reading the paper and for their helpful comments. The authors would also like to thank the referee for the valuable comments and suggestions.
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