Skip to main content
SpringerLink
Log in

Two-weighted estimates for p-adic Riesz potential and its commutators on Morrey–Herz spaces

  • Original Paper
  • Published:
Fractional Calculus and Applied Analysis Aims and scope Submit manuscript

Abstract

In this paper, we study the boundedness of p-adic Riesz potential on two-weighted Morrey–Herz spaces with both power weight and Muckenhoupt weight. Moreover, the boundedness for commutators of p-adic Riesz potential with symbols in Lipschitz spaces and weighted central BMO spaces on such spaces are also established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Albeverio, S., Khrennikov, A.Yu.: Shelkovich, V.M.: Harmonic analysis in the \(p\)-adic Lizorkin spaces: fractional operators, pseudo-differential equations, \(p\)-wavelets. Tauberian theorems. J. Fourier Anal. Appl. 12, 393–425 (2006)

  2. Chuong, N.M.: Pseudodifferential Operators and Wavelets over Real and \(p\)-adic Fields. Springer–Basel (2018)

  3. Chuong, N.M., Egorov, Yu.V., Khrennikov, A.Yu., Meyer, Y., Mumford, D.: Harmonic, Wavelet and \(p\)-Adic Analysis. World Scientific (2007)

  4. Chuong, N.M., Duong, D.V.: Wavelet bases in the Lebesgue spaces on the field of \(p\)-adic numbers. \(p\)-Adic Numbers Ultrametric Anal. Appl. 5, 106–121 (2013)

  5. Chuong, N.M., Co, N.V.: The Cauchy problem for a class of pseudo-differential equations over \(p\)-adic field. J. Math. Anal. Appl. 340, 629–643 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chuong, N.M., Duong, D.V., Dung, K.H.: Weighted estimates for maximal operators, Riesz potential operators and commutators on \(p\)-adic Lebesgue and Morrey spaces. \(p\)-Adic numbers, Ultrametric Anal. Appl. 11, 123–134 (2019)

  7. Chuong, N.M., Hung, H.D.: Maximal functions and weighted norm inequalities on local fields. Appl. Comput. Harmon. Anal. 29, 272–286 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Duong, D.V., Hong, N.T.: Some new weighted estimates for \(p\)-adic multilinear Hausdorff type operator and its commutators on Morrey-Herz spaces. Adv. Oper. Theory. 7(3), 1–21 (2022)

    MathSciNet  MATH  Google Scholar 

  9. Dragovich, B.: \(p\)-Adic and adelic cosmology: \(p\)-adic origin of dark energy and dark matter, \(p\)-adic mathematical physics. AIP Conf. Proc. 826, 25–42 (2006)

    Article  MATH  Google Scholar 

  10. Grafakos, L.: Modern Fourier Analysis. Second Edition, Springer (2008)

  11. Haran, S.: Riesz potentials and explicit sums in arithmetic. Invent. Math. 101, 697–703 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  12. Haran, S.: Analytic potential theory over the \(p\)-adics. Ann. Inst. Fourier (Grenoble) 43, 905–944 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hensel, K.: Über eine neue Begründung der Theorie der algebraischen Zahlen. Jahresbericht der Deutschen Mathematiker-Vereinigung. 6(3), 83–88 (1987)

    MATH  Google Scholar 

  14. Hytönen, T., Pérez, C., Rela, E.: Sharp reverse Hölder property for \(A_{\infty }\) weights on spaces of homogeneous type. J. Funct. Anal. 263, 3883–3899 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Khrennikov, A.Yu.: \(p\)-Adic Valued Distributions in Mathematical Physics. Kluwer Academic Publishers, Dordrecht-Boston-London (1994)

  16. Khrennikov, A. Yu, Oleschko, K.: Applications of \(p\)-adic numbers: from physics to geology. Advances in Non-Archimedean Analysis, American Mathematical Society (AMS), 121–131 (2016)

  17. Kim, Y.C.: A simple proof of the \(p\)-adic version of the Sobolev embedding theorem. Commun. Korean. Math. Soc. 25, 27–36 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kochubei, A.N.: Schrödinger-type operator over \(p\)-adic number field. Theoretical and Mathematical Physics. 86(3), 221–228 (1991)

    Article  MathSciNet  Google Scholar 

  19. Kozyrev, S.V.: Methods and applications of ultrametric and \(p\)-adic analysis: From wavelet theory to biophysics. Proc. Steklov Inst. Math. 274, 1–84 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mo, H., Wang, X., Ma, R.: Commutator of Riesz potential in \(p\)-adic generalized Morrey spaces. Front. Math. China 13, 633–645 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  21. Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165, 207–226 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  22. Nakai, E.: Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces. Math. Nachr. 165(1), 95–103 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ruzhansky, M., Suragan, D., Yessirkegenov, N.: Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces. Fract. Calc. Appl. Anal. 21(3), 577–612 (2018). https://doi.org/10.1515/fca-2018-0032

    Article  MathSciNet  MATH  Google Scholar 

  24. Samko, N.: Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces. Fract. Calc. Appl. Anal. 24(6), 1643–1669 (2021). https://doi.org/10.1515/fca-2021-0071

    Article  MathSciNet  MATH  Google Scholar 

  25. Sarfraz, S., Aslam, M.: Some estimates for \(p\)-adic fractional integral operator and its commutators on \(p\)-adic Herz spaces with rough kernels, Fract. Calc. Appl. Anal. 25, 1734–1755 (2022) https://doi.org/10.1007/s13540-022-00064-w

  26. Shi, Y.L., Shi,Y.F., Chen, S.B.: \(p\)-Adic Riesz potential and its commutators on Morrey–Herz spaces. J. Funct. Spaces. 2022, Article ID 7227544, 11 pages (2022)

  27. Stein, E.M.: Harmonic Analysis. Orthogonality, and Oscillatory Integrals. Princeton University Press, Real-variable Methods (1993)

    Google Scholar 

  28. Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press (1970)

  29. Taibleson, M.H.: Fourier Analysis on Local Fields. Princeton University Press, Princeton, NJ, USA, University of Tokyo Press, Tokyo, Japan (1975)

    MATH  Google Scholar 

  30. Vladimirov, V.S., Volovich, I.V.: \(p\)-Adic quantum mechanics. Comm. Math. Phys. 123, 659–676 (1989)

    Article  MathSciNet  MATH  Google Scholar 

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

  32. Volosivets, S.S.: Maximal function and Reisz potential on \(p\)-adic linear spaces. \(p-\)Adic Numbers Ultrametric Anal. Appl. 5, 226–234 (2013)

  33. Volosivets, S.S.: Generalized fractional integrals in \(p\)-adic Morrey and Herz spaces. \(p\)-Adic Numbers Ultrametric Anal. Appl. 9, 53–61 (2017)

  34. Wu, Q.Y., Fu, Z.W.: Hardy–Littlewood–Sobolev inequalities on \(p\)-adic central Morrey spaces. J. Funct. Spaces and Appl. 2015, Article ID 419532, 7 pages (2015)

Download references

Acknowledgements

The authors would like to express their sincere thanks to the anonymous referees for several valuable comments and suggestions to improve the paper.

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam

    Ngo Thi Hong

  2. Vietnam National University, Ho Chi Minh City, Vietnam

    Ngo Thi Hong

  3. School of Mathematics, Mientrung University of Civil Engineering, Phu Yen, Vietnam

    Ngo Thi Hong & Dao Van Duong

Authors
  1. Ngo Thi Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dao Van Duong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dao Van Duong.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Thi Hong, N., Van Duong, D. Two-weighted estimates for p-adic Riesz potential and its commutators on Morrey–Herz spaces. Fract Calc Appl Anal 26, 2618–2650 (2023). https://doi.org/10.1007/s13540-023-00205-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13540-023-00205-9

Keywords

Mathematics Subject Classification

Search

Navigation