A note on multilinear pseudo-differential operators and iterated commutators
Bull. Korean Math. Soc. 2020 Vol. 57, No. 4, 851-864
Published online April 20, 2020
Printed July 31, 2020
Yongming Wen, Huoxiong Wu, Qingying Xue
Xiamen University; Xiamen University; Ministry of Education
Abstract : 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)
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