Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Parabolic Marcinkiewicz integrals associated to polynomials compound curves and extrapolation

Feng Liu and Daiqing Zhang

Shandong University of Science and Technology, Xiamen University

Abstract

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

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