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J. Korean Math. Soc. 2021; 58(4): 1035-1058

Online first article November 27, 2020      Printed July 1, 2021

https://doi.org/10.4134/JKMS.j200450

Copyright © The Korean Mathematical Society.

Weighted estimates for certain rough operators with applications to vector valued inequalities

Feng Liu, Qingying Xue

Shandong University of Science and Technology; Ministry of Education

Abstract

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Under certain rather weak size conditions assumed on the kernels, some weighted norm inequalities for singular integral operators, related maximal operators, maximal truncated singular integral operators and Marcinkiewicz integral operators in nonisotropic setting will be shown. These weighted norm inequalities will enable us to obtain some vector valued inequalities for the above operators.

Keywords: Nonisotropic singular integrals, Marcinkiewicz integrals, rough kernels, weighted norm inequalities, vector valued inequalities

MSC numbers: Primary 42B20, 42B25

Supported by: This work was financially supported by NNSF of China (Nos. 11701333, 11671039, 11871101) and NSFC-DFG (No. 11761131002).

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