본문 바로가기
KERD
논문KCI 등재

Parameter Marcinkiewicz integral and its commutator on generalized Orlicz-Morrey spaces

Guanghui Lu
대한수학회 (The Korean Mathematical Society)|2021.03|대한수학회지 (Journal of the KMS)|제58권 제2호|pp. 383-400|DOI 10.4134/JKMS.j200071

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

commutatorParameter Marcinkiewicz integralLipschits space$\mathrm{BMO}$ spacegeneralized Orlicz-Morrey
주제분류수학

초록

The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator $\mathcal{M}^{\rho}_{\Omega, b}$ which is generated by the parameter Marcinkiwicz integral $\mathcal{M}^{\rho}_{\Omega}$ and the Lipschitz function $b$ on generalized Orlicz-Morrey space $L^{\Phi,\varphi}(\mathbb{R}^{d})$ in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral $\mathcal{M}^{\rho}_{\Omega}$ on the $L^{\Phi,\varphi}(\mathbb{R}^{d})$, and the commutator $[b,\mathcal{M}^{\rho}_{\Omega}]$ generated by the $\mathcal{M}^{\rho}_{\Omega}$ and the space $\mathrm{BMO}$ on the $L^{\Phi,\varphi}(\mathbb{R}^{d})$, are also obtained, respectively.

Abstract

The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator $\mathcal{M}^{\rho}_{\Omega, b}$ which is generated by the parameter Marcinkiwicz integral $\mathcal{M}^{\rho}_{\Omega}$ and the Lipschitz function $b$ on generalized Orlicz-Morrey space $L^{\Phi,\varphi}(\mathbb{R}^{d})$ in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral $\mathcal{M}^{\rho}_{\Omega}$ on the $L^{\Phi,\varphi}(\mathbb{R}^{d})$, and the commutator $[b,\mathcal{M}^{\rho}_{\Omega}]$ generated by the $\mathcal{M}^{\rho}_{\Omega}$ and the space $\mathrm{BMO}$ on the $L^{\Phi,\varphi}(\mathbb{R}^{d})$, are also obtained, respectively.

참고문헌 (32)

  1. H. Al-Qassem, "Lp bounds for the function of Marcinkiewicz", Mathematical Research Letters, 9(5), pp.697~700 (2002), International Press of Boston[DOI]
  2. A. P. Calderon, "COMMUTATORS OF SINGULAR INTEGRAL OPERATORS", Proceedings of the National Academy of Sciences, 53(5), pp.1092~1099 (1965), Proceedings of the National Academy of Sciences[DOI]
  3. Yanping Chen, "Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels", Forum Mathematicum, 27(4), pp.2087~2111 (2015), Walter de Gruyter GmbH[DOI]
  4. Yan Ping Chen, "Commutators of Marcinkiewicz integral with rough kernels on Sobolev spaces", Acta Mathematica Sinica, English Series, 27(7), pp.1345~1366 (2011), Springer Science and Business Media LLC[DOI]
  5. R. R. Coifman, "Factorization Theorems for Hardy Spaces in Several Variables", The Annals of Mathematics, 103(3), pp.611~ (1976), JSTOR[DOI]
  6. Fatih Deringoz, "Characterizations for the Riesz potential and its commutators on generalized Orlicz-Morrey spaces", Journal of Inequalities and Applications, 2016(1), pp.22~ (2016), Springer Science and Business Media LLC[DOI]
  7. Fatih Deringoz, "A characterization for Adams-type boundedness of the fractional maximal operator on generalized Orlicz–Morrey spaces", Integral Transforms and Special Functions, 28(4), pp.284~299 (2017), Informa UK Limited[DOI]
  8. F. Deringoz, "Operator theory, operator algebras and applications", pp.2014, Birkh¨auser
  9. R. A. DeVore, "Maximal functions measuring smoothness", Mem. Amer. Math. Soc, 47(293), pp.viii~115 (1984)[DOI]
  10. Yong Ding, "Marcinkiewicz integral on hardy spaces", Integral Equations and Operator Theory, 42(2), pp.174~182 (2002), Springer Science and Business Media LLC[DOI]
  11. Yong Ding, "Existence and Boundedness of Parametrized Marcinkiewicz Integral with Rough Kernel on Campanato Spaces", Nagoya Mathematical Journal, 181, pp.103~148 (2006), Cambridge University Press (CUP)[DOI]
  12. D. Fan, "Weak type (1, 1) estimates for Marcinkiewicz integrals with rough kernels", Tohoku Math. J, 53(2), pp.265~284 (2001)[DOI]
  13. WENHUA GAO, "Boundedness for Marcinkiewicz integrals associated with Schrödinger operators", Proceedings - Mathematical Sciences, 124(2), pp.193~203 (2014), Springer Science and Business Media LLC[DOI]
  14. Vagif S. Guliyev, "Some Characterizations of Lipschitz Spaces via Commutators on Generalized Orlicz–Morrey Spaces", Mediterranean Journal of Mathematics, 15(4), pp.19~ (2018), Springer Science and Business Media LLC[DOI]
  15. Lars Hörmander, "Estimates for translation invariant operators in Lp spaces", Acta Mathematica, 104(1-2), pp.93~140 (1960), International Press of Boston[DOI]
  16. Guoen Hu, "On the commutator of the Marcinkiewicz integral", Journal of Mathematical Analysis and Applications, 283(2), pp.351~361 (2003), Elsevier BV[DOI]
  17. Svante Janson, "Mean oscillation and commutators of singular integral operators", Arkiv för Matematik, 16(1-2), pp.263~270 (1978), International Press of Boston[DOI]
  18. Bo Li, "Parametric Marcinkiewicz integrals with rough kernels acting on weak Musielak–Orlicz Hardy spaces", Banach Journal of Mathematical Analysis, 13(1), pp.47~63 (2019), Springer Science and Business Media LLC[DOI]
  19. S. Z. Lu, "Boundedness of commutators for the Marcinkiewicz integrals", Acta Math. Sinica (Chin. Ser.), 49(3), pp.481~490 (2006)
  20. G. Lu, "Estimates for parameter Littlewood-Paley g ∗κ functions on nonhomogeneous metric measure spaces", J. Funct. Spaces, 2016, pp.12~ (2016)[DOI]
  21. S. Lu, "The central BMO spaces and Littlewood-Paley operators,", Approx. Theory Appl. (N.S.), 11(3), pp.72~94 (1995)
  22. J. Marcinkiewicz, "Sur quelques int´egrals du type de Dini", Ann. Soc. Polon. Math, 17, pp.42~50 (1938)
  23. S. P. Tao, "Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent", Analysis in Theory and Applications, 31(1), pp.13~24 (2019), Global Science Press[DOI]
  24. M. Sakamoto, "Boundedness of Marcinkiewicz functions", Studia Math, 135(2), pp.103~142 (1999)
  25. 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]
  26. Alberto Torchinsky, "A note on the Marcinkiewicz integral", Colloquium Mathematicum, 60(1), pp.235~243 (1990), Institute of Mathematics, Polish Academy of Sciences[DOI]
  27. L. Wang, "Higher order commutators of Marcinkiewicz integral operator on Herz-Morrey spaces with variable exponent", Acta Math. Sinica, China Ser, 49(3), pp.481~490 (2006)
  28. 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]
  29. Y. M. Ying, "A note on the Marcinkiewicz integral operator with rough kernel on product spaces", Chinese Ann. Math. Ser. A, 24(6), pp.777~786 (2003)
  30. Pu Zhang, "Characterization of Lipschitz spaces via commutators of the Hardy–Littlewood maximal function", Comptes Rendus Mathematique, 355(3), pp.336~344 (2017), Elsevier BV[DOI]
  31. Z. S. Zhang, "A note on the L2 boundedness of Marcinkiewicz integral operator", Int. J. Math. Comput, 26(4), pp.133~137 (2015)
  32. F. Y. Zhao, "A note on commutators of the Marcinkiewicz integral", J. Math. (Wuhan), 29(6), pp.784~788 (2009)

관련 논문AI추천

Higher-order commutators of parameterized Littlewood-Paley operators on two weight Herz spaces with variable exponentsQi Wu, Yanqi Yang대한수학회 · 대한수학회지2025 · 제62권 제2호SOME ESTIMATES FOR GENERALIZED COMMUTATORS OF MULTILINEAR CALDERÓN-ZYGMUND OPERATORSHonghai Liu, Ling Wang, Zengyan Si대한수학회 · 대한수학회보2023 · 제60권 제2호Weak boundedness for the commutator of $n$-dimensional rough Hardy operator on homogeneous Herz spaces and central Morrey spacesDunyan Yan, Lei Ji, Mingquan Wei대한수학회 · 대한수학회보2024 · 제61권 제4호On the oscillatory operators of Calder\'on type commutators on Morrey spacesHuoxiong Wu, Weijin Yan대한수학회 · 대한수학회보2025 · 제62권 제5호ON CERTAIN ESTIMATES FOR ROUGH GENERALIZED PARAMETRIC MARCINKIEWICZ INTEGRALSDaiqing Zhang대한수학회 · 대한수학회보2023 · 제60권 제1호Multilinear commutators of multilinear square operators associated with new $BMO$ functions and new weight functionsChunliang Li, Shuhui Yang, Yan Lin대한수학회 · 대한수학회보2025 · 제62권 제2호

이 간행물의 다른 논문 (12건)

Invariance of kneading matrix under conjugacyChaitanya Gopalakrishna, Murugan Veerapazhampp. 265-281A graded minimal free resolution of the $m$-th order symbolic power of a star configuration in $\P^n$신용수, 박정필pp. 283-308PRIMENESS AND PRIMITIVITY IN NEAR-RINGSGerhard Wendtpp. 309-326Complete convergence for weighted sums of AANA random variables and its application in nonparametric regression modelsYajing Zhang, Aiting Shenpp. 327-349Monoidal functors and exact sequences of groups for Hopf quasigroupsJose N. Alonso Alvarez, Ramon Gonzalez Rodriguez, Jose M. Fernandez Vilaboapp. 351-381
원문 보기