Have a personal or library account? Click to login
RETRACTED: Sharp and Weighted Boundedness for Multilinear Integral Operators Cover

RETRACTED: Sharp and Weighted Boundedness for Multilinear Integral Operators

By: Xiuyun Xia,  Huatao Chen,  Hao Tian,  Ye Wang and  Yadan Shi  
Open Access
|Oct 2024

References

  1. CHANG, A. C.: Weighted boundedness of multilinear integral operators for the endpoint cases,AIMS Math. 7 (2022), 5690–5711.
  2. CHEN, D. Z.: Weighted boundedness for Toeplitz type operator related to singular integral transform with variable Calderón-Zygmund kernel,AIMS Math. 6 (2021), 688–697.
  3. CHEN, D. Z.: Weighted boundedness of multilinear pseudo-differential operators,AIMS Math. 6 (2021), 12698–12712.
  4. CHANILLO, S.: A note on commutators, Indiana Univ. Math. J. 31 (1982), 7–16.
  5. CHIARENZA, F.—FRASCA, M.: Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat. Appl 7 (1987), 273–279.
  6. COHEN, J.: A sharp estimate for a multilinear singular integral on Rn, Indiana Univ. Math. J. 30 (1981), no. 5, 693–702.
  7. COHEN, J.—GOSSELIN, J.: On multilinear singular integral operators on Rn, Studia Math. 72 (1982), 199–223.
  8. COHEN, J.—GOSSELIN, J.: Az BMO estimate for multilinear singular integral operators, Illinois J. Math. 30 (1986), no, 3, 445–464, DOI: 10.1215/ijm/1256044539.
  9. COIFMAN, R.—MEYER, Y.: Wavelets, Calderon-Zygmund and Multilinear Operators. Cambridge Studies in Advanced Math. 48, Cambridge University Press, Cambridge, 1997.
  10. COIFMAN, R—ROCHBERG, R.: Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), no. 2, 249–254.
  11. DI FAZIO, G.—RAGUSA, M. A.: Commutators and Morrey spaces, Boll. Un. Mat. Ital. A(7) (5) (1991), no. 3, 323–332.
  12. DI FAZIO, G.—RAGUSA, M. A.: Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients, J. Func. Anal. 112 (1993), no. 2, 241–256.
  13. GARCIA-CUERVA, J.—RUBIO DE FRANCIA, J. L.: Weighted Norm Inequalities and Related Topics. North-Holland Mathematics Studies, Vol. 116. Notas de Matemática [Mathematical Notes], 104. North-Holland Publishing Co., Amsterdam, 1985.
  14. HU, G.—YANG, D. C.: A variant sharp estimate for multilinear singular integral operators, Studia Math. 141 (2000), no. 1, 25–42.
  15. LIU, L. Z.: Boundedness of multilinear singular integral operators satisfying a variant of Hormander’s condition and mean oscillation, Analysis and Mathematical Physics 6 (2016), 345–363.
  16. LIU, L. Z.: Weighted boundedness for Toeplitz type operators associated to singular integral operator with non-smooth kernel, Filomat 30 (2016), no. 9, 2489–2502.
  17. LIU, L. Z.: Boundedness of multilinear singular integral operator with non-smooth kernels and mean oscillation,Quaest. Math. 40 (2017), 295–312.
  18. HU, HAIJUN—LIU, LANZHE: Weighted inequalities for a general commutator associated to a singular integral operator satisfying a variant of Hörmander’s condition,Math. Notes 101 (2017), no. 5–6, 830–840.
  19. TAN, Y. X.—LIU, L. Z.: Weighted boundedness of multilinear operator associated to singular integral operator with variable Calderón-Zygmund kernel, Rev. R. Acad. Cienc. Exactas, Fis. Nat. Ser. A Mat. RACSAM 111 (2017), no. 4, 931–946.
  20. TAN, Y. X.—LIU, L. Z.: Boundedness of Toeplitz operators related to singular integral operators, Izv. Ross. Akad. Nauk Ser. Mat. 82 (2018), no. 6, 158–171; [Translation in: Izv. Math. 82 (2018), no. 6, 1225–1238.]
  21. MIZUHARA, T.: Boundedness of some classical operators on generalized Morrey spaces. In: Proceedings of The Conference held in Sendai, Japan, 1990, Harmonic analysis (Sendai, 1990), ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991, pp. 183–189,
  22. PEETRE, J.: On convolution operators leaving Lp,λ-spaces invariant, Ann. Mat. Pura Appl. 72 (1966), no. 4, 295–304.
  23. PEETRE, J.: On the theory of Lp,λ-spaces, J. Funct. Anal. 4 (1969), 71–87.
  24. PÉREZ, C.—PRADOLINI, G.: Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J. 49 (2001), no. 1 23–37.
  25. PÉREZ, C.—TRUJILLO-GONZALEZ, R.: Sharp weighted estimates for multilinear commutators, J. London Math. Soc. (2) 65 (2002), no. 3, 672–692.
  26. STEIN, E. M.: Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals. [With the assistance of Timothy S. Murphy.] Princeton Mathematical Series, Vol. 43. Monogr. Harmon Anal., III. Princeton Univ. Press, Princeton, NJ, 1993.
  27. TORCHINSKY, A.: Real-Variable Methods in Harmonic Analysis. In: Pure and Applied Math., Vol. 123. Academic Press, Inc., Orlando, FL, 1986.
  28. TORCHINSKY, A.—WANG, S.: A note on the Marcinkiewicz integral, Colloq. Math. 60/61 (1990), no. 1, 235–243.
DOI: https://doi.org/10.2478/tmmp-2024-0017 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 185 - 204
Submitted on: May 9, 2024
Accepted on: Jun 18, 2024
Published on: Oct 20, 2024
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 Xiuyun Xia, Huatao Chen, Hao Tian, Ye Wang, Yadan Shi, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.