Abstract
We find a concrete integral formula for the class of generalized Toeplitz operators \(T_a\) in Bergman spaces \(A^p\), \(1<p<\infty \), studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an \(L^2\)-symbol a such that \(T_{|a|} \) fails to be bounded in \(A^2\), although \(T_a : A^2 \rightarrow A^2\) is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical one whenever the latter makes sense.
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Taskinen, J., Virtanen, J. On generalized Toeplitz and little Hankel operators on Bergman spaces. Arch. Math. 110, 155–166 (2018). https://doi.org/10.1007/s00013-017-1124-2
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DOI: https://doi.org/10.1007/s00013-017-1124-2