Bull. Korean Math. Soc. 2015; 52(3): 771-788
Printed May 31, 2015
https://doi.org/10.4134/BKMS.2015.52.3.771
Copyright © The Korean Mathematical Society.
Feng Liu and Daiqing Zhang
Shandong University of Science and Technology, Xiamen University
In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the $L^p$ bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.
Keywords: Marcinkiewicz integrals, rough kernels, mixed homogeneity, extrapolation
MSC numbers: Primary 42B20; Secondary 42B25, 42B99
2018; 55(2): 659-672
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