L<SUP>p</SUP> BOUNDS FOR THE PARABOLIC LITTLEWOOD-PALEY OPERATOR ASSOCIATED TO SURFACES OF REVOLUTION
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In this paper the authors study the Lp boundedness for parabolic Littlewood-Paley operator $${\mu}{\Phi},{\Omega}(f)(x)=\({\int}_{0}^{\infty}{\mid}F_{\Phi,t}(x){\mid}^2\frac{dt}{t^3}\)^{1/2}$$, where $$F_{\Phi,t}(x)={\int}_{p(y){\leq}t}\frac{\Omega(y)}{\rho(y)^{{\alpha}-1}}f(x-{\Phi}(y))dy$$ and ${\Omega}$ satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.
Abstract
In this paper the authors study the Lp boundedness for parabolic Littlewood-Paley operator $${\mu}{\Phi},{\Omega}(f)(x)=\({\int}_{0}^{\infty}{\mid}F_{\Phi,t}(x){\mid}^2\frac{dt}{t^3}\)^{1/2}$$, where $$F_{\Phi,t}(x)={\int}_{p(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.
참고문헌 (10)
- A. Benedek, "Convolution operators on Banach space valued functions", Proc. Natl. Acad. Sci. U.S.A., 48, pp.356~365 (1962)
- Y. Chen, "The parabolic Littlewood-Paley operator with Hardy space kernels", Canad. Math. Bull, 52(4), pp.521~534 (2009)
- Y. Ding, "Lp boundedness of Marcinkiewicz integrals with Hardy space function kernels", Acta Math. Sin. (Engl. Ser.), 16(4), pp.593~600 (2000)
- Y. Ding, "Lp bounds for Marcinkiewicz integrals", Proc. Edinb. Math. Soc.(2), 46(3), pp.669~677 (2003)
- E. Fabes, "Singular integrals with mixed homogeneity", Studia Math, 27, pp.19~38 (1966)
- L. Grafakos, "Convolution Calderon-Zygmund singular integral operators with rough kernel", Indiana Univ. Math. J, 47, pp.455~469 (1998)
- A. Nagel, "On Hilbert transforms along curves. II", Amer. J. Math, 98(2), pp.395~403 (1976)
- E. M. Stein, "On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz", Trans. Amer. Math. Soc, 88, pp.430~466 (1958)
- E. M. Stein, "Problems in harmonic analysis related to curvature", Bull. Amer. Math. Soc, 84(6), pp.1239~1295 (1978)
- Q. Xue, "Parabolic Littlewood-Paley g-function with rough kernels", Acta Math. Sin. (Engl. Ser.), 24(12), pp.2049~2060 (2008)