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We consider the Kato-Ponce type inequality for bilinear pseudo-differential operators with $S_{0,0}$-type symbols in the scale of Besov spaces. In particular, the borderline whether the boundedness of those operators holds or not is discussed.

Kato-Ponce type inequality for bilinear pseudo-differential operators of $S_{0, 0}$-type in the scale of Besov spaces