A note on generalized parametric Marcinkiewicz integrals
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In the present paper, we establish certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels in Grafakos-Stefanov class $\mathcal{F}_\beta({\rm S}^{n-1})$. Our main results improve and generalize a result given by Al-Qassem, Cheng and Pan in 2012. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g_\lambda^{*}$-functions and area integrals are also presented.
Abstract
In the present paper, we establish certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels in Grafakos-Stefanov class $\mathcal{F}_\beta({\rm S}^{n-1})$. Our main results improve and generalize a result given by Al-Qassem, Cheng and Pan in 2012. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g_\lambda^{*}$-functions and area integrals are also presented.
참고문헌 (32)
- H. M. Al-Qassem, "Boundedness of rough integral operators on Triebel-Lizorkin spaces", Publicacions Matemàtiques, 56, pp.261~277 (2012), Universitat Autonoma de Barcelona[DOI]
- H. Al-Qassem, "On rough generalized parametric Marcinkiewicz integrals", Journal of Mathematical Inequalities, (3), pp.763~780 (2007), Element d.o.o.[DOI]
- H. Al-Qassem, "{${\large\bf L}^{\large\bf p}$ bounds for the function of Marcinkiewicz", Mathematical Research Letters, 9(5), pp.697~700 (2002), International Press of Boston[DOI]
- A. Benedek, "CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS", Proceedings of the National Academy of Sciences, 48(3), pp.356~365 (1962), Proceedings of the National Academy of Sciences[DOI]
- J. Chen, "A note on a Marcinkiewicz integral operator", Math. Nachr, 227, pp.33~42 (2001)
- Jiecheng Chen, "Singular integral operators on function spaces", Journal of Mathematical Analysis and Applications, 276(2), pp.691~708 (2002), Elsevier BV[DOI]
- Yong Ding, "L p -Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels", Acta Mathematica Sinica, English Series, 16(4), pp.593~600 (2000), Springer Science and Business Media LLC[DOI]
- Y. Ding, "On the Lp boundedness of Marcinkiewicz integrals", Michigan Math. J, 50(1), pp.17~26 (2002)[DOI]
- Y. Ding, "Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces", Tohoku Math. J. (2), 62(2), pp.233~262 (2010)[DOI]
- Dashan Fan, "On the Generalized Marcinkiewicz Integral Operators with Rough Kernels", Canadian Mathematical Bulletin, 54(1), pp.100~112 (2011), Canadian Mathematical Society[DOI]
- L. Grafakos, "Classical Fourier Analysis" (2008), Springer
- Loukas Grafakos, "L^p bounds for singular integrals and maximal singular integrals with rough kernels", Indiana University Mathematics Journal, 47(2), pp.0~0 (1998), Indiana University Mathematics Journal[DOI]
- Lars Hörmander, "Estimates for translation invariant operators in Lp spaces", Acta Mathematica, 104(1-2), pp.93~140 (1960), International Press of Boston[DOI]
- Hung Viet Le, "Singular integrals with mixed homogeneity in Triebel–Lizorkin spaces", Journal of Mathematical Analysis and Applications, 345(2), pp.903~916 (2008), Elsevier BV[DOI]
- Feng Liu, "Integral operators of Marcinkiewicz type on Triebel-Lizorkin spaces", Mathematische Nachrichten, 290(1), pp.75~96 (2017), Wiley[DOI]
- Feng Liu, "On the Triebel-Lizorkin space boundedness of Marcinkiewicz integrals along compound surfaces", Mathematical Inequalities & Applications, (2), pp.515~535 (1998), Element d.o.o.[DOI]
- Feng Liu, "A note of Littlewood-Paley functions on Triebel-Lizorkin spaces", 대한수학회보, 55(2), pp.659~672 (2018), 대한수학회
- FENG LIU, "A NOTE ON MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION", Journal of the Australian Mathematical Society, 104(3), pp.380~402 (2018), Cambridge University Press (CUP)[DOI]
- Feng Liu, "Boundedness and continuity of maximal operators associated to polynomial compound curves on Triebel-Lizorkin spaces", Mathematical Inequalities & Applications, 22(1), pp.25~44 (1998), Element d.o.o.[DOI]
- Feng Liu, "Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces", Frontiers of Mathematics in China, 14(1), pp.95~122 (2019), Springer Science and Business Media LLC[DOI]
- Feng Liu, "A rough Marcinkiewicz integral along smooth curves", Journal of Nonlinear Sciences and Applications, 09(06), pp.4450~4464 (2016), International Scientific Research Publications MY SDN. BHD.[DOI]
- FENG LIU, "BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES", Journal of the Australian Mathematical Society, 99(3), pp.380~398 (2015), Cambridge University Press (CUP)[DOI]
- Feng Liu, "$$L^p$$ L p bounds for Marcinkiewicz integrals associated to homogeneous mappings", Monatshefte für Mathematik, 181(4), pp.875~906 (2016), Springer Science and Business Media LLC[DOI]
- Feng Liu, "L^p bounds for parametric Marcinkiewicz integrals with mixed homogeneity", Mathematical Inequalities & Applications, 18(2), pp.453~469 (1998), Element d.o.o.[DOI]
- Feng Liu, "Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces", Science China Mathematics (2020), Springer Science and Business Media LLC[DOI]
- Feng Liu, "PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION", 대한수학회보, 52(3), pp.771~788 (2015), 대한수학회
- M. Sakamoto, "Boundedness of Marcinkiewicz functions", Studia Math, 135(2), pp.103~142 (1999)
- E. M. Stein, "On the Functions of Littlewood-Paley, Lusin, and Marcinkiewicz", Transactions of the American Mathematical Society, 88(2), pp.430~466 (1958), JSTOR[DOI]
- E. M. Stein, "Harmonic analysis: real-variable methods, orthogonality, and oscillatory inte-grals" (1993), Princeton University Press
- Huoxiong Wu, "On Marcinkiewicz Integral Operators with Rough Kernels", Integral Equations and Operator Theory, 52(2), pp.285~298 (2005), Springer Science and Business Media LLC[DOI]
- Huoxiong Wu, "Lp bounds for Marcinkiewicz integrals associated to surfaces of revolution", Journal of Mathematical Analysis and Applications, 321(2), pp.811~827 (2006), Elsevier BV[DOI]
- Kôzô Yabuta, "Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces", Applied Mathematics-A Journal of Chinese Universities, 30(4), pp.418~446 (2015), Springer Science and Business Media LLC[DOI]
