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Maximal Operators of Multilinear Singular Integrals on Weighted Hardy Type Spaces

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Abstract

In this paper, the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces, which essentially extend and improve the previous known results obtained by Grafakos and Kalton (2001) and Li, Xue and Yabuta (2011). The corresponding estimates on variable Hardy spaces are also established.

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References

  1. Andersen, K. and John, R. T., Weighted inequalities for vector-valued maximal functions and singular integrals, Studio, Math., 69(1), 1980/81, 19–31.

    Article  MathSciNet  MATH  Google Scholar 

  2. Coifman, R., A real variable characterization of Hp, Studia Math., 51, 1974, 269–274.

    Article  MathSciNet  MATH  Google Scholar 

  3. Coifman, R. and Weiss, G., Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc, 83(4), 1977, 569–645.

    Article  MathSciNet  MATH  Google Scholar 

  4. Cruz-Uribe, D. and Fiorenza, A., Variable Lebesgue Spaces: Foundations and Harmonic Analysis, Springer-Verlag, Basel, 2013.

    Book  MATH  Google Scholar 

  5. Cruz-Uribe, D., Moen, K. and Nguyen, H. V., Multilinear fractional Calderón-Zygmund operators on weighted Hardy spaces, Houston J. Math., 45(3), 2019, 853–871.

    MathSciNet  MATH  Google Scholar 

  6. Cruz-Uribe, D., Moen, K. and Nguyen, H. V., The boundedness of multilinear Calderón-Zygmund operators on weighted and variable Hardy spaces, Publ. Mat., 63(2), 2019, 679–713.

    Article  MathSciNet  MATH  Google Scholar 

  7. Cruz-Uribe, D., Moen, K. and Nguyen, H. V., A new approach to norm inequalities on weighted and variable Hardy spaces, Ann. Acad. Sci. Fenn. Math., 45, 2020, 175–198.

    Article  MathSciNet  MATH  Google Scholar 

  8. Cruz-Uribe, D. and Naibo, V., Kato-Ponce inequalities on weighted and variable Lebesgue spaces, Differential Integral Equations., 29(9–10), 2016, 801–836.

    MathSciNet  MATH  Google Scholar 

  9. Cruz-Uribe, D. and Wang, L.-A., Variable Hardy spaces, Indiana Univ. Math. J., 63(2), 2014, 447–493.

    Article  MathSciNet  MATH  Google Scholar 

  10. Fefferman, C. and Stein, E., Hp spaces of several variables, Acta Math., 129(3–4), 1972, 137–193.

    Article  MathSciNet  MATH  Google Scholar 

  11. García-Cuerva, L., Weighted Hp spaces, Disserlaiiones Math. (Rozpramy Mat.), 162, 1979, 63 pp.

  12. Gatto, A. B., Gutiérrez, C. F. and Wheeden, R. L., Fractional integrals on weighted Hp spaces, Trans. Amer. Math. Soc, 289(2), 1985, 575–589.

    MathSciNet  MATH  Google Scholar 

  13. Grafakos, L. and Kalton, N. J., Multilinear Calderón-Zygmund operators in Hardy spaces, Collect. Math., 52(2), 2001, 169–180.

    MathSciNet  MATH  Google Scholar 

  14. Grafakos, L., Nakamura., S., Nguyen, H. V. and Sawano, Y., Conditions for boundedness into Hardy spaces, Math. Nachr., 292(11), 2019, 2383–2410.

    Article  MathSciNet  MATH  Google Scholar 

  15. Grafakos, L., Nakamura, S., Nguyen, H. V. and Sawano, Y., Multiplier conditions for boundedness into Hardy spaces, Ann. Inst. Fourier, 71(3), 2021, 1047–1064.

    Article  MathSciNet  MATH  Google Scholar 

  16. Hart, J. and Oliveira, L., Hardy space estimates for limited ranges of Muckenhoupt weights, Adv. Math., 313, 2017, 803–838.

    Article  MathSciNet  MATH  Google Scholar 

  17. Li, W., Xue, Q. and Yabuta, K., Multilinear Calderón-Zygmund operators on weighted Hardy spaces, Studia Math., 199(1), 2010, 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, W., Xue, Q. and Yabuta, K., Maximal operator for multilinear Calderón-Zygmund singular integral operators on weighted Hardy spaces, J. Math. Anal. Appt., 373(2), 2011, 384–392.

    Article  MATH  Google Scholar 

  19. Lu, G. and Zhu, Y., Bounds of singular integrals on weighted Hardy spaces and discrete Littlewood-Paley analysis, J. Geom. Anal, 22(3), 2012, 666–684.

    Article  MathSciNet  MATH  Google Scholar 

  20. Nakai, E. and Sawano, Y., Hardy spaces with variable exponents and generalized Campanato spaces, J. Fund. Anal, 262(9), 2012, 3665–3748.

    Article  MathSciNet  MATH  Google Scholar 

  21. Rocha, P. and Urcitiolo, M., Fractional type integral operators on variable Hardy spaces, Acta. Math. Hungar., 143(2), 2014, 502–514.

    Article  MathSciNet  Google Scholar 

  22. Ströerg, J.-O. and Torchinsky, A., Weighted Hardy Spaces, Springer-Verlag, Berlin, New York, 1989, OCLC: 298624160.

    Book  Google Scholar 

  23. Orlicz, W., Über konjugierte exponentenfolgen, Studio, Math., 3, 1931, 200–211.

    Article  MATH  Google Scholar 

  24. Tan, J., Bilinear Calderón-Zygmund operators on products of variable Hardy spaces. Forum Math., 31(1), 2019, 187–198.

    Article  MathSciNet  MATH  Google Scholar 

  25. Tan, J., Multilinear fractional type operators and their commutators on Hardy spaces with variable exponents, Anal. Math. Phys., 10 (4), 2020, 16pp.

  26. Tan, J. and Zhao, J., Multilinear pseudo-differential operators on product of local Hardy spaces with variable exponents, J. Pseudo-Differ. Oper. Appl, 10(2), 2019, 379–396.

    Article  MathSciNet  MATH  Google Scholar 

  27. Xue, Q. and Yan, J., Multilinear version of reversed Hölder inequality and its applications to multilinear Calderón-Zygmund operators, J. Math. Soc. Japan., 64(4), 2012, 1053–1069.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, 363000, China

    Yongming Wen

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Huoxiong Wu

  3. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Qingying Xue

  4. Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China

    Qingying Xue

Authors
  1. Yongming Wen
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  2. Huoxiong Wu
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  3. Qingying Xue
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Corresponding author

Correspondence to Yongming Wen.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11871101, 12171399), NSFC-DFG (No. 11761131002), the Natural Science Foundation of Fujian Province (No. 2021J05188), the Scientific Research Project of The Education Department of Fujian Province (No. JAT200331), the President’s fund of Minnan Normal University (No. KJ2020020), the Institute of Meteorological Big Data-Digital Fujian, Fujian Key Laboratory of Data Science and Statistics and Fujian Key Laboratory of Granular Computing and Applications (Minnan Normal University).

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Wen, Y., Wu, H. & Xue, Q. Maximal Operators of Multilinear Singular Integrals on Weighted Hardy Type Spaces. Chin. Ann. Math. Ser. B 44, 391–406 (2023). https://doi.org/10.1007/s11401-023-0022-0

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  • DOI: https://doi.org/10.1007/s11401-023-0022-0

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