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Lp BOUNDS FOR THE PARABOLIC MARCINKIEWICZ INTEGRAL WITH ROUGH KERNELS
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 Title & Authors
Lp BOUNDS FOR THE PARABOLIC MARCINKIEWICZ INTEGRAL WITH ROUGH KERNELS
Chen, Yanping; Ding, Yong;
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 Abstract
We prove the $L^p(1. The result is an improvement and extension of some known results.
 Keywords
parabolic Marcinkiewicz integrals;mixed homogeneity space;rough kernel;
 Language
English
 Cited by
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Lp boundedness for commutators of parabolic Littlewood-Paley operators with rough kernels, Mathematische Nachrichten, 2011, 284, 8-9, 973  crossref(new windwow)
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L p Bounds for the Commutator of Parabolic Singular Integral with Rough Kernels, Potential Analysis, 2007, 27, 4, 313  crossref(new windwow)
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Rough Marcinkiewicz integrals with mixed homogeneity on product spaces, Acta Mathematica Sinica, English Series, 2013, 29, 7, 1231  crossref(new windwow)
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PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION, Bulletin of the Korean Mathematical Society, 2015, 52, 3, 771  crossref(new windwow)
7.
BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES, Journal of the Australian Mathematical Society, 2015, 99, 03, 380  crossref(new windwow)
8.
Parabolic Marcinkiewicz integrals along surfaces on product domains, Acta Mathematica Sinica, English Series, 2011, 27, 1, 1  crossref(new windwow)
 References
1.
A. AL-Salman, H. AL-Qassem, L. Cheng, and Y. Pan, LP bounds for the function of Marcinkiewicz, Math. Res. Lett. 9 (2002), no. 5-6, 697-700 crossref(new window)

2.
A. Benedek, A. Calderon, and R. Panzone, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 356-365 crossref(new window)

3.
A. Calderon and A. Zygmund, A note on the interpolation of sublinear operations, Amer. J. Math. 78 (1956), 282-288 crossref(new window)

4.
Y. Ding, D. Fan, and Y. Pan, Weighted boundedness for a class of rough Marcinkiewicz integrals, Indiana Univ. Math. J. 48 (1999), no. 3, 1037-1055

5.
Y. Ding, D. Fan, and Y. Pan, $L^p$-boundedness of Marcinkiewicz integrals with Hardy space function kernels, Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 4, 593-600 crossref(new window)

6.
Y. Ding, Q. Xue and K. Yabuta, Parabolic Littlewood-Paley g-function with rough kernels, preprint

7.
J. Duoandikoetxea and J. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), no. 3, 541-561 crossref(new window)

8.
E. Fabes and N. Riviere, Singular integrals with mixed homogeneity, Studia Math. 27 (1966), 19-38

9.
W. R. Madych, On Littlewood-Paley functions, Studia Math. 50 (1974), 43-63

10.
A. Nagel, N. Riviere and S. Wainger, On Hilbert transforms along curves. II., Amer. J. Math. 98 (1976), no. 2, 395-403 crossref(new window)

11.
F. Ricci and E. Stein, Multiparameter singular integrals and maximal functions, Ann. Inst. Fourier (Grenoble) 42 (1992), no. 3, 637-670 crossref(new window)

12.
E. Stein, On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958) 430-466 crossref(new window)

13.
E. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239-1295 crossref(new window)

14.
T. Walsh, On the function of Marcinkiewicz, Studia Math. 44 (1972), 203-217