Toeplitz operators with BMO symbols and the Berezin transform - Nina Zorboska (International Journal of Mathematics and Mathematical Sciences)
We prove that the boundedness and compactness of the Toeplitz operator on the Bergman space with a BMO1 symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends the known results in the cases when the symbol is either a positive L1-function or an L∞ function.