Bull. Korean Math. Soc. 2012; 49(4): 787-797
Printed July 1, 2012
https://doi.org/10.4134/BKMS.2012.49.4.787
Copyright © The Korean Mathematical Society.
Feixing Wang, Yanping Chen, and Wei Yu
University of Science and Technology Beijing, University of Science and Technology Beijing, University of Science and Technology Beijing
In this paper the authors study the $L^p$ boundedness for parabolic Littlewood-Paley operator $$ \mu_{\Phi,\Omega}(f)(x)=\left(\int_0^\infty|F_{\Phi,t}(x)|^{2}\frac{dt}{t^{3}}\right)^{1/2}, $$ where $$ F_{\Phi,t}(x)=\int_{\rho(y)\leq t} {\frac{\Omega(y)}{\rho(y)^{\alpha-1}}f(x-\Phi(y))dy} $$ and $\Omega$ satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.
Keywords: parabolic Littlewood-Paley operator, rough kernel, surfaces of revolution
MSC numbers: 42B20, 42B25
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