Lp BOUNDS FOR THE PARABOLIC LITTLEWOOD-PALEY OPERATOR ASSOCIATED TO SURFACES OF REVOLUTION

Title & Authors
Lp BOUNDS FOR THE PARABOLIC LITTLEWOOD-PALEY OPERATOR ASSOCIATED TO SURFACES OF REVOLUTION
Wang, Feixing; Chen, Yanping; Yu, Wei;

Abstract
In this paper the authors study the $\small{L^p}$ boundedness for parabolic Littlewood-Paley operator {\mu}{\Phi},{\Omega}(f)(x)
Keywords
parabolic Littlewood-Paley operator;rough kernel;surfaces of revolution;
Language
English
Cited by
1.
PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION,;;

대한수학회보, 2015. vol.52. 3, pp.771-788
1.
PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION, Bulletin of the Korean Mathematical Society, 2015, 52, 3, 771
References
1.
A. Benedek, A. Calderon, and R. Panzone, Convolution operators on Banach space valued functions, Proc. Natl. Acad. Sci. U.S.A. 48 (1962), 356-365.

2.
Y. Chen and Y. Ding, The parabolic Littlewood-Paley operator with Hardy space kernels, Canad. Math. Bull. 52 (2009), no. 4, 521-534.

3.
Y. Ding, D. Fan, and Y. Pan, Lp boundedness of Marcinkiewicz integrals with Hardy space function kernels, Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 4, 593-600.

4.
Y. Ding and Y. Pan, Lp bounds for Marcinkiewicz integrals, Proc. Edinb. Math. Soc. (2) 46 (2003), no. 3, 669-677.

5.
E. Fabes and N. Riviere, Singular integrals with mixed homogeneity, Studia Math. 27 (1966), 19-38.

6.
L. Grafakos and A. Stefanov, Convolution Calderon-Zygmund singular integral operators with rough kernel, Indiana Univ. Math. J. 47 (1998), 455-469.

7.
A. Nagel, N. Riviere, and S. Wainger, On Hilbert transforms along curves. II, Amer. J. Math. 98 (1976), no. 2, 395-403.

8.
E. M. Stein, On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430-466.

9.
E. M. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239-1295.

10.
Q. Xue, Y. Ding, and K. Yabuta, Parabolic Littlewood-Paley g-function with rough kernels, Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 12, 2049-2060.