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ON CERTAIN ESTIMATES FOR ROUGH GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALS

Daiqing Zhang
대한수학회 (The Korean Mathematical Society)|2023.01|대한수학회보 (Bulletin of the KMS)|제60권 제1호|pp. 47-73|DOI 10.4134/BKMS.b210850

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참고문헌

키워드

Generalized parametric Marcinkiewicz integralpolynomial compound curverough kernelhomogeneous Triebel-Lizorkin space
주제분류수학

초록

This paper is devoted to establishing certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels given by $h\in\Delta_\gamma(\mathbb{R}_{+})$ and $\Omega\in W\mathcal{F}_\beta({\rm S}^{n-1})$ for some $\gamma,\,\beta\in(1,\infty]$. 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

This paper is devoted to establishing certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels given by $h\in\Delta_\gamma(\mathbb{R}_{+})$ and $\Omega\in W\mathcal{F}_\beta({\rm S}^{n-1})$ for some $\gamma,\,\beta\in(1,\infty]$. 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 (25)

  1. H. Al-Qassem, "Boundedness of rough integral operators on Triebel-Lizorkin spaces", Publ. Mat, 56(2), pp.261~277 (2012)
  2. H. Al-Qassem, "On rough generalized parametric Marcinkiewicz integrals", Journal of Mathematical Inequalities, (3), pp.763~780 (2017), Element d.o.o.[DOI]
  3. Hussain Al-Qassem, "On certain estimates for Marcinkiewicz integrals and extrapolation", Collectanea mathematica, 60(2), pp.123~145 (2009), Springer Science and Business Media LLC[DOI]
  4. H. Al-Qassem, "Lp bounds for the function of Marcinkiewicz", Mathematical Research Letters, 9(5), pp.697~700 (2002), International Press of Boston[DOI]
  5. 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]
  6. J. Chen, "A note on a Marcinkiewicz integral operator", Math. Nachr, 227, pp.33~42 (2001)
  7. Jiecheng Chen, "Singular integral operators on function spaces", Journal of Mathematical Analysis and Applications, 276(2), pp.691~708 (2002), Elsevier BV[DOI]
  8. 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]
  9. Yong Ding, "On the LP boundedness of Marcinkiewicz integrals", Michigan Mathematical Journal, 50(1) (2002), Michigan Mathematical Journal[DOI]
  10. Yong Ding, "Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces", Tohoku Mathematical Journal, 62(2) (2010), Mathematical Institute, Tohoku University[DOI]
  11. Dashan Fan, "A note on singular integrals associated with a variable surface of revolution", Mathematical Inequalities & Applications, (2), pp.441~454 (2009), Element d.o.o.[DOI]
  12. Dashan Fan, "On the Generalized Marcinkiewicz Integral Operators with Rough Kernels", Canadian Mathematical Bulletin, 54(1), pp.100~112 (2011), Canadian Mathematical Society[DOI]
  13. 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]
  14. Lars Hörmander, "Estimates for translation invariant operators in Lp spaces", Acta Mathematica, 104(1-2), pp.93~140 (1960), International Press of Boston[DOI]
  15. 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]
  16. Wenjuan Li, "Boundedness of singular integrals associated to surfaces of revolution on Triebel–Lizorkin spaces", Forum Mathematicum, 28(1), pp.57~75 (2014), Walter de Gruyter GmbH[DOI]
  17. Feng Liu, "Integral operators of Marcinkiewicz type on Triebel–Lizorkin spaces", Mathematische Nachrichten, 290(1), pp.75~96 (2016), Wiley[DOI]
  18. Feng Liu, "A note on generalized parametric Marcinkiewicz integrals", 대한수학회보, 56(5), pp.1099~1115 (2019), 대한수학회[DOI]
  19. Feng Liu, "Inequalities for generalized parametric Marcinkiewicz integrals along polynomial compound curves", Journal of Mathematical Inequalities, (1), pp.187~209 (2020), Element d.o.o.[DOI]
  20. Huoxiong Wu, "Rough singular integrals and maximal operators with mixed homogeneity along compound curves", Mathematische Nachrichten, 287(10), pp.1166~1182 (2014), Wiley[DOI]
  21. Feng Liu, "L^p bounds for parametric Marcinkiewicz integrals with mixed homogeneity", Mathematical Inequalities & Applications, (2), pp.453~469 (2015), Element d.o.o.[DOI]
  22. M. Sakamoto, "Boundedness of Marcinkiewicz functions", Studia Math, 135(2), pp.103~142 (1999)
  23. E. M. Stein, "On the Functions of Littlewood-Paley, Lusin, and Marcinkiewicz", Transactions of the American Mathematical Society, 88(2), pp.430~ (1958), JSTOR[DOI]
  24. 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]
  25. 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]

관련 논문AI추천

A note on generalized parametric Marcinkiewicz integralsFeng Liu대한수학회 · 대한수학회보2019 · 제56권 제5호WEIGHTED Lp-BOUNDEDNESS OF SINGULAR INTEGRALS WITH ROUGH KERNEL ASSOCIATED TO SURFACESHuoxiong Wu, Ronghui Liu대한수학회 · 대한수학회지2021 · 제58권 제1호Singular and Marcinkiewicz integral operators on product domainsAhmad Al-Salman, Badriya Al-Azri대한수학회 · 대한수학회논문집2023 · 제38권 제2호PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATIONDaiqing Zhang, Feng Liu대한수학회 · 대한수학회보2015 · 제52권 제3호A Note on Marcinkiewicz Integral Operators on Product DomainsAhmad Al-Salman, Badriya Al-Azri경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제4호L<SUP>p</SUP> BOUNDS FOR THE PARABOLIC LITTLEWOOD-PALEY OPERATOR ASSOCIATED TO SURFACES OF REVOLUTIONFeixing Wang, Wei Yu, Yanping Chen대한수학회 · 대한수학회보2012 · 제49권 제4호

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