A ug 2 00 7 Boundedness and Compactness of Toeplitz operators with L 1 symbols on the Bergman Space ∗
نویسنده
چکیده
We characterise the boundedness of a Toeplitz operator on the Bergman space with a L symbol. We also prove that the compactness of a Toeplitz operator on the Bergman space with a L symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends known results in the cases when the symbol is either a positive L function, an L∞ function or a general BMO function.
منابع مشابه
Spectral theory of Toeplitz and Hankel operators on the Bergman space A^1
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 ari...
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