Skip to main content
SpringerLink
Log in

Multipliers for global Morrey spaces

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

Based on a new approach for a wide class of global Morrey spaces, we give an exact description of the multiplier space between two Morrey spaces from this class. It is shown that in this case the multiplier space for a couple of Morrey spaces is an approximation Morrey space structurally constructed from the original spaces.

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

Data availability

No datasets were generated or analysed during the current study.

References

  1. Appell, J., Zabrejko, P.P.: Nonlinear Superposition Operators. Cambridge University Press, Cambridge (1990)

    Book  MATH  Google Scholar 

  2. Bennett, G.: Factorizing the classical inequalities. Memoirs of the American Mathematical Society, vol. 120, American Mathematical Society, Providence (1996)

  3. Berezhnoi, E.I.: A discrete varsion of local Morrey spaces. Izvestiya RAN: Ser. Mat. 81(1), 3–31 (2017). ((in Russian). English transl.: Izvestiya: Mathematics. 81(1), 1–28 (2017))

  4. Berezhnoi, E.I.: Geometric properties of the space \( \varphi (X, Y) \). Func. anal. i ego pril. 18(1), 59–60 (1984). [(in Russian). English transl.: Functional Analysis and its Applications 18, no. 1, 48–50 (1984). 10.1007/BF01076362]

  5. Berezhnoi, E.I.: Calculation of the Calderón–Lozanovski\(\breve{i}\) construction for a couple of local Morrey spaces. Eurasian Math. J. 11(3), 21–34 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  6. Berezhnoi, E.I.: On Reflexivity and Other Geometric Properties of Morrey Spaces. Operator Theory and Harmonic Analysis. Part 1. New General Trends and Advances of the Theory. Springer Proceedings in Mathematics and Statistics, vol. 357, 119–136

  7. Berezhnoi, E.I.: Multipliers for local Morrey spaces. Positivity 5 (2022) https://doi.org/10.1007/s11117-022-00951-9

  8. Berezhnoi, E.I.: Multipliers for Calderón’s Construction. Functional Analysis and Its Applications, To apper

  9. Berezhnoi, E.I., Maligranda, L.: Representation of Banach ideal spaces and factorization of operators. Can. J. Math. 57(5), 897–940 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Calderón, A.P.: Intermediate spaces and interpolation, the complex method. Stud. Math. 24, 113–190 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  11. Delgado, O., Sanchez Perez, E.A.: Summability properties for multiplication operators on Banach function spaces. Integral Equ. Oper. Theory 66(2), 197–214 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Nauka, Moscow, 1977 (Russian). English transl. Pergamon Press, Oxford-Elmsford, New York, 1982, xiv+589 pp

  13. Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise multipliers of Calderón–Lozanovski\(\breve{i}\) spaces. Math. Nachr. 286(8–9), 876–907 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise products of some Banach function spaces and factorization. J. Funct. Anal. 266(2), 616–659 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kufner, A., Maligranda, L., Persson, L.-E.: The Hardy Inequality. About its History and Some Related Results, Pilsen (2007)

  16. Lemarie-Rieusset, P.G.: Multipliers and Morrey spaces. Potencial Anal. 38(3), 741–752 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lemarie-Rieusset, P.G.: Erratum to: Multipliers and Morrey spaces. Potencial Anal. 41(4), 1359–1362 (2014)

    Article  MATH  Google Scholar 

  18. Leśnik, K., Tomaszewski, J.: Pointwise multipliers of Orlicz function spaces and factorization. Positivity 21(4), 1563–1573 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces. I. Sequence Spaces. Springer, Berlin (1977)

  20. Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces. II. Function Spaces. Springer, Berlin (1979)

    Book  MATH  Google Scholar 

  21. Maligranda, L.: Orlicz Spaces and Interpolation. Sem. Mat., vol. 5, University of Campinas, Campinas, SP, Brazil (1989)

  22. Maurey, B.: Theoremes de factorisation pour les operateurs lineaires a valeurs dans les espaces \(L_p\). Asterisque 11, 1–163 (1974)

    MATH  Google Scholar 

  23. Nakai, E.: Pointwise multipliers on several functions spaces: a survey. Linear Nonlinear Anal. 3(1), 27–59 (2017)

    MathSciNet  MATH  Google Scholar 

  24. Nakai, E., Sawano, Y.: Spaces of pointwise multipliers on Morrey spaces and weak Morrey spaces. Mathematics 9, 2754 (2021). https://doi.org/10.3390/math9212754

    Article  Google Scholar 

  25. Schep, A.R.: Products and factors of Banach function spaces. Positivity 14, 301–319 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research was partially supported by the Ministry of Education and Science of the Russian Federation project 075-02-2023-924.

Funding

Not applicable.

Author information

Author notes

  1. Evgenii I. Berezhnoi

    Present address: , 14, Sovetskaya St., Yaroslavl, Russian Federation, 150000

Authors and Affiliations

  1. Department of Mathematics, Yaroslavl State University, 14, Sovetskaya St., Yaroslavl, Russian Federation, 150000

    Evgenii I. Berezhnoi

  2. Reginal Mathematical Center of Southern Federal University, 105/42 Bolshaya Sadovaya, Rostov-on-Don, Russian Federation, 344090

    Evgenii I. Berezhnoi

Authors
  1. Evgenii I. Berezhnoi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All results belong to the author.

Corresponding author

Correspondence to Evgenii I. Berezhnoi.

Ethics declarations

Competing interests:

No competing interests.

Ethics approval:

Not applicable.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Berezhnoi, E.I. Multipliers for global Morrey spaces. Positivity 27, 42 (2023). https://doi.org/10.1007/s11117-023-00994-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11117-023-00994-6

Keywords

Mathematics Subject Classification

Search

Navigation