We first introduce Condition (L) and (B) to describe the bounded Toeplitz operator $T_g$ with integrable symbols on the regular weighted Bergman space $L^1_a(/omega)$.  In addition, we discuss the boundedness and compactness of the Toeplitz operator $T_/mu$ from $L_{h}^{p}(/omega)$ to $L_{h}^{q}(/omega)$ for $1<p, q</infty$, where $/mu$ is a positive Borel measure. This is joint with Kunyu Guo, Siyu Wang and Zipeng Wang

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