Boundedness and Compactness of Toeplitz operators with L^1 symbols on the Bergman space

Details Boundedness and Compactness of Toeplitz operators with L^1 symbols on the Bergman space Boundedness and Compactness of Toeplitz operators with L^1 symbols on the Bergman space

2007-08-20

arxiv.org/abs/0708.2611v1

Mathematics

Complex Variables

13 pages

Scientific paper

We characterise the boundedness of a Toeplitz operator on the Bergman space with an L^1 symbol.We also prove that the compactness of a Toeplitz operator on the Bergman space with an L^1 symbol is completely determined by the boundary behaviour of itss Berezin transform. This result extends known results in the cases when the symbol is either a positive L^1 function, an L^\infty function or a general BMO^1 function.

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