A ug 2 00 7 Boundedness and Compactness of Toeplitz operators with L 1 symbols on the Bergman Space ∗

نویسنده

  • Dieudonne Agbor
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.

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تاریخ انتشار 2008