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The Hausdorff Operator on Weighted p-Adic Morrey and Herz Type Spaces

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Abstract

In the present article, we come up with the boundedness of Hausdorff operator, defined by means of linear transformation A, on the weighted p-adic Morrey and weighted p-adic Herz type spaces. Also, by imposing some special conditions on A, we discuss the sharpness of the results presented in this article.

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References

  1. V. I. Burenkov and E. Liflyand, “On the boundedness of Hausdorff operators on Morrey-type spaces,” Eurasian Math. J. 8, 97–104 (2017).

    MathSciNet  Google Scholar 

  2. J. Chen, J. Dai, D. Fan and X. Zhu, “Boundedness of Hausdorff operators on Lebesgue spaces and Hardy spaces,” Sci. China Math. 61, 1647–1664 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Chen, S. He and X. Zhu, “Boundedness of Hausdorff operators on the power weighted Hardy spaces,” Appl. Math. 32, 462–476 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  4. N. M. Chung and D. V. Duong, “The p-adic weighted Hardy-Cesaro operators on weighted Morrey-Herz space,” p-Adic Numbers Ultrametric Anal. Appl. 8, 204–216 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  5. N. M. Chung, H. D. Hung and N. T. Hong, “Bounds of p-adic weighted Hardy-Cesaro operator and their commutators on p-adic weighted spaces of Morrey types,” p-Adic Numbers Ultrametric Anal. Appl. 8,31–44 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Fan and F. Zhao, “Sharp constants for multivariate Hausdorff q-inequalities,” J. Aust. Math. Soc. 106 (2), 274–286 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Hussain and A. Ajaib, “Some weighted inequalities for Hausdorff operators and commutators,” J. Inequal. Appl. 2018 (2018) 6, 19 pages.

    Google Scholar 

  8. D. Q. Huy and L. D. Ky, “The multi-parameter Hausdorff operators on H 1 and L p,” Math. Inequal. Appl. 21, 497–510 (2018).

    MathSciNet  MATH  Google Scholar 

  9. A. Lerner and E. Liflyand, “Multidimensional Hausdorff operators on the real Hardy spaces,” J. Austr. Math. Soc. 83, 79–86 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Liflyand, “Hausdorff operators on Hardy spaces,” Eurasian Math. J. 4, 101–141 (2013).

    MathSciNet  MATH  Google Scholar 

  11. E. Liflyand and A. Miyachi, “Boundedness of multidimensional Hausdorff operators in H p spaces, 0 <p < 1,” Trans. Amer. Math. Soc. 371, 4793–4814 (2019).

    Article  MathSciNet  Google Scholar 

  12. E. Liflyand and A. Miyachi, “Boundedness of the Hausdorff operators in H p spaces, 0 <p < 1,” Stud. Math. 194, 279–292 (2009).

    Article  MATH  Google Scholar 

  13. E. Liflyand and F. Mórecz, “The Hausdorff operator is bounded on the real Hardy space H 1(ℝ),” Proc. Amer. Math. Soc. 128, 1391–1396 (2000).

    Article  MathSciNet  Google Scholar 

  14. N. Sarfraz and A. Hussain, “Estimates for the commutators of p-adic Hausdorff operator on Herz-Morrey spaces,” Mathematics 7 (2), (2019) 127, 15 pages.

    Article  Google Scholar 

  15. J. Ruan, D. Fan and Q. Wu, “Weighted Herz space estimates for Hausdorff operators on the Heisenberg group,” Banach J. Math. Anal. 11, 513–535 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  16. S. S. Volosivets, “Multidimensinal Hausdorff operator on p-adic fields,” p-Adic Numbers Ultrametric Anal. Appl. 2, 252–259 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  17. S. S. Volosivets, “Hausdorff operators on p-adic linear spaces and their properties in Hardy, BMO, and Hölder spaces,” Math. Notes 93, 382–391 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  18. S. S. Volosivets, “Weak and strong estimates for rough Hausdorff type operator defined on p-adic linear space,” p-Adic Numbers Ultrametric Anal. Appl. 9, 236–241 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  19. V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-Adic Analysis and Mathematical Physics (World Scientific, Singapore, 1994).

    Book  MATH  Google Scholar 

  20. Q. Wu and Z. Fu, “Boundedness of Hausdorff operators on Hardy spaces in the Heisenberg group,” Banach J. Math. Anal. 12, 909–934 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Xiao, “L p and BMO bounds of weighted Hardy-Littlewood averages,” J. Math. Anal. Appl. 262, 660–666 (2001).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Amjad Hussain or Naqash Sarfraz.

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Hussain, A., Sarfraz, N. The Hausdorff Operator on Weighted p-Adic Morrey and Herz Type Spaces. P-Adic Num Ultrametr Anal Appl 11, 151–162 (2019). https://doi.org/10.1134/S2070046619020055

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  • DOI: https://doi.org/10.1134/S2070046619020055

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