Spectral theory of Toeplitz and Hankel operators on the Bergman space A^1
نویسندگان
چکیده
The Fredholm properties of Toeplitz operators on the Bergman space A have been well-known for continuous symbols since the 1970s. We investigate the case p = 1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on A that arise when we no longer have 1 < p < ∞; in particular bounded Toeplitz operators on A were characterized completely very recently but only for bounded symbols. We also consider compactness of Hankel operators on A.
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These are the notes of the lecture course given at LTCC in 2015. The aim of the course is to consider the following three classes of operators: Toeplitz and Hankel operators on the Hardy space on the unit circle and Toeplitz operators on the Bergman space on the unit disk. For each of these three classes of operators, we consider the following questions: boundedness and estimates or explicit ex...
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