Bulletin of the
Korean Mathematical Society BKMS

This paper gives a sparse domination for the iterated commutators of multilinear pseudo-differential operators with the symbol $\sigma$ belonging to the H\"ormander class, and establishes the quantitative bounds of the Bloom type estimates for such commutators. Moreover, the $C_p$ estimates for the corresponding multilinear pseudo-differential operators are also obtained.

Keywords: Multilinear pseudo-differential operator, commutators, sparse operators, weighted $BMO$, $C_p$ weights

MSC numbers: Primary 47G30, 42B20; Secondary 42B25, 46E30

Supported by: This work is financially supported by the NSFC (Nos. 11771358, 11671039, 11871101) and NSFC-DFG (No. 11761131002)