Lp BOUNDS FOR THE PARABOLIC MARCINKIEWICZ INTEGRAL WITH ROUGH KERNELS

Title & Authors
Lp BOUNDS FOR THE PARABOLIC MARCINKIEWICZ INTEGRAL WITH ROUGH KERNELS
Chen, Yanping; Ding, Yong;

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 1. PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION,;; 대한수학회보, 2015. vol.52. 3, pp.771-788 1. Boundedness of Marcinkiewicz integrals with mixed homogeneity along compound surfaces, Journal of Inequalities and Applications, 2014, 2014, 1, 265 2. Boundedness of parabolic singular integrals and Marcinkiewicz integrals on Triebel-Lizorkin spaces, Analysis in Theory and Applications, 2011, 27, 1, 59 3. Lp boundedness for commutators of parabolic Littlewood-Paley operators with rough kernels, Mathematische Nachrichten, 2011, 284, 8-9, 973 4. L p Bounds for the Commutator of Parabolic Singular Integral with Rough Kernels, Potential Analysis, 2007, 27, 4, 313 5. Rough Marcinkiewicz integrals with mixed homogeneity on product spaces, Acta Mathematica Sinica, English Series, 2013, 29, 7, 1231 6. PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION, Bulletin of the Korean Mathematical Society, 2015, 52, 3, 771 7. BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES, Journal of the Australian Mathematical Society, 2015, 99, 03, 380 8. Parabolic Marcinkiewicz integrals along surfaces on product domains, Acta Mathematica Sinica, English Series, 2011, 27, 1, 1 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 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 3. A. Calderon and A. Zygmund, A note on the interpolation of sublinear operations, Amer. J. Math. 78 (1956), 282-288 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

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