Toeplitz operators with L^1 symbols on the weighted Bergman spaces

This paper characterizes the boundedness and compactness of aToeplitz operator on the weighted Bergman space with a L1 symbol.This result extends known results in the cases when the symbol is eithera positive L1 function, an L∞ function or a general BMO1 function.In addition, we also give some estimates about the norm and essentialnorm of Toeplitz operators with L1 symbols.