On the Bergman space of the unit disk, we consider a class of operators which contain sums of finitely many Toeplitz products with harmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. Our results provide a unified way of treating several known results.
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Boo Rim Choe, Hyungwoon Koo, Young Joo Lee, Sums of Toeplitz products with harmonic symbols. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 43–70DOI 10.4171/RMI/529