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 $L^p$ bounds for the parabolic Littlewood-Paley operator associated to surfaces of revolution Bull. Korean Math. Soc. 2012 Vol. 49, No. 4, 787-797 https://doi.org/10.4134/BKMS.2012.49.4.787Printed July 1, 2012 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 Abstract : 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 Downloads: Full-text PDF