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In this paper, the ranges of bilinear pseudo-differential operators of$S_{0,0}$-type on $L^2 \times L^2$ are determined in the framework of Besovspaces. Our result improves the $L^2 \times L^2 \to L^1$ boundedness of thoseoperators with symbols in the bilinear H\"ormander class $BS^m_{0,0}$.

On the ranges of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2 \times L^2$