Skip to main content
SpringerLink
Log in

A Refinement of the Adams Theorem on the Riesz Potential

  • Conference paper
  • First Online:
Operator Theory and Harmonic Analysis (OTHA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 357))

  • 654 Accesses

Abstract

The goal of this note is to consider the application of the complex interpolation space of Morrey spaces. Actually, the boundedness of Riesz potentials acting on Morrey spaces, which is obtained by Adams, is refined by means of the complex interpolation.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Adams, D.R.: A note on Riesz potentials. Duke Math. J. 42, 765–778 (1975)

    Article  MathSciNet  Google Scholar 

  2. Bergh, J., Löfström, J.: Interpolation spaces. An introduction. Grundlehren der Mathematischen Wissenschaften, No. 223. Springer, Berlin-New York (1976)

    Google Scholar 

  3. Bergh, J.: Relation between the 2 complex methods of interpolation. Indiana Univ. Math. J. 28(5), 775–778 (1979)

    Article  MathSciNet  Google Scholar 

  4. Hakim, D.I., Sawano, Y.: Interpolation of generalized Morrey spaces. Rev. Mat. Complut. 29(2), 295–340 (2016)

    Article  MathSciNet  Google Scholar 

  5. Hakim, D.I.: Complex interpolation of certain closed subspaces of Morrey spaces. Tokyo J. Math. 41(2), 487–514 (2018)

    Article  MathSciNet  Google Scholar 

  6. Hakim, D.I., Sawano, Y.: Calderón’s first and second complex interpolation of closed subspaces of Morrey spaces. J. Fourier Anal. Appl. 23(5), 1195–1226 (2017)

    Article  MathSciNet  Google Scholar 

  7. Lemarié-Rieusset, P.G.: Multipliers and Morrey spaces. Potential Anal. 38(3), 741–752 (2013)

    Article  MathSciNet  Google Scholar 

  8. Lemarié-Rieusset, P.G.: Erratum to: Multipliers and Morrey spaces. Potential Anal. 41(4), 1359–1362 (2014)

    Article  MathSciNet  Google Scholar 

  9. Lu, Y.F., Yang, D., Yuan, W.: Interpolation of Morrey spaces on metric measure spaces. Can. Math. Bull. 57(3), 598–608 (2014)

    Article  MathSciNet  Google Scholar 

  10. Mastyło, M., Sawano, Y.: Complex interpolation and Calderón–Mityagin couples of Morrey spaces. Anal. PDE 12(7), 1711–1740 (2019)

    Article  MathSciNet  Google Scholar 

  11. Sawano, Y., Di Fazio, G., Hakim, D.I.: Morrey Spaces Introduction and Applications to Integral Operators and PDE’s, vol. I. CRC Press, Boca Raton (2020)

    MATH  Google Scholar 

  12. Sawano, Y., Di Fazio, G., Hakim, D.I.: Morrey Spaces Introduction and Applications to Integral Operators and PDE’s, vol. II. CRC Press, Boca Raton (2020)

    MATH  Google Scholar 

  13. Sawano, Y., Sugano, S.: Complex interpolation and the Adams theorem. Potential Analysis 54(2), 299–305 (2021)

    Article  MathSciNet  Google Scholar 

  14. Sawano, Y., Sugano, S., Tanaka, H.: Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces. Trans. Am. Math. Soc. 363(12), 6481–6503 (2011)

    Article  MathSciNet  Google Scholar 

  15. Sawano, Y., Sugano, S., Tanaka, H.: Orlicz–Morrey spaces and fractional operators. Potential Anal. 36(4), 517–556 (2012)

    Article  MathSciNet  Google Scholar 

  16. Shestakov, V.A.: On complex interpolation of Banach spaces of measurable functions. Vestnik Leningrad. Univ. 19, 64–68 (1974)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author was supported by Grant-in-Aid for Scientific Research (C) (No. 19K03546), the Japan Society for the Promotion of Science.

Author information

Authors and Affiliations

  1. Graduate School of Science and Engineering, Chuo University, Kasuga, Tokyo, Japan

    Yoshihiro Sawano

  2. People’s Friendship University of Russia, Moscow, Russia

    Yoshihiro Sawano

Authors
  1. Yoshihiro Sawano
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoshihiro Sawano .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Mechanic and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

    Alexey N. Karapetyants

  2. Department of Mathematics, Cinvestav, Santiago de Queretaro, Querétaro, Mexico

    Vladislav V. Kravchenko

  3. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Elijah Liflyand

  4. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Helmuth R. Malonek

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sawano, Y. (2021). A Refinement of the Adams Theorem on the Riesz Potential. In: Karapetyants, A.N., Kravchenko, V.V., Liflyand, E., Malonek, H.R. (eds) Operator Theory and Harmonic Analysis. OTHA 2020. Springer Proceedings in Mathematics & Statistics, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-030-77493-6_29

Download citation

Publish with us

Policies and ethics

Search

Navigation