Skip to main content
SpringerLink
Log in

B σ-Campanato Estimates for Commutators of Calderón–Zygmund Operators

  • Conference paper
  • First Online:
Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 236))

Abstract

In the earlier papers [16, 19], the Bσ-function spaces were introduced for the purpose of unifying central Morrey spaces, λ-central mean oscillation spaces and usual Morrey–Campanato spaces.

The purpose of this paper is to establish the Bσ-Campanato estimates for commutators of Calderón-Zygmund operators on Bσ-Morrey spaces.

Mathematics Subject Classification (2010). Primary 42B35; Secondary 46E35, 46E30, 26A33.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.R. Adams, A note on Rieszp otentials. Duke Math. J. 42 (1975), no. 4, 765–778.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Alvarez, M. Guzmán-Partida and J. Lakey, Spaces of bounded λ-central mean oscillation, Morrey spaces, and λ-central Carleson measures. Collect. Math. 51 (2000), 1–47.

    MathSciNet  MATH  Google Scholar 

  3. A. Beurling, Construction and analysis of some convolution algebra. Ann. Inst. Fourier 14 (1964), 1–32.

    Article  MathSciNet  MATH  Google Scholar 

  4. Y. Chen and K. Lau, Some new classes of Hardy spaces. J. Func. Anal. 84 (1989), 255–278.

    Article  MathSciNet  MATH  Google Scholar 

  5. F. Chiarenza and M. Frasca, Morrey spaces and Hardy–Littlewood maximal function. Rend. Mat. Appl. 7 (1987), no. 3-4, 273–279.

    MathSciNet  MATH  Google Scholar 

  6. R.R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables. Ann. of Math. 103 (1976), 611–635.

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Di Fazio and M.A. Ragusa, Commutators and Morrey spaces. Bollettino U. M. I. 5-A (1991), no. 7, 255–278.

    Google Scholar 

  8. H. Feichtinger, An elementary approach to Wiener’s third Tauberian theorem on Euclidean n-space. Proceedings of Conference at Cortona 1984, Symposia Mathematica 29, Academic Press, New York, 1987, 267–301.

    Google Scholar 

  9. Z. Fu, Y. Lin and S. Lu, λ-central BMO estimates for commutators of singular integral operators with rough kernels. Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 3, 373–386

    Google Scholar 

  10. J. García-Cuerva, Hardy spaces and Beurling algebras. J. London Math. Soc. (2) 39 (1989), 499–513.

    Google Scholar 

  11. J. García-Cuerva and M.J.L. Herrero, A theory of Hardy spaces associated to the Herzsp aces. Proc. London Math. Soc. 69 (1994), 605–628.

    Article  MathSciNet  MATH  Google Scholar 

  12. L. Grafakos, X. Li and D. Yang, Bilinear operators on Herz-type Hardy spaces. Trans. Amer. Math. Soc. 350 (1998), 1249–1275.

    Article  MathSciNet  MATH  Google Scholar 

  13. C. Herz, Lipschitzsp aces and Bernstein’s theorem on absolutely convergent Fourier transforms. J. Math. Mech. 18 (1968), 283–324.

    MathSciNet  MATH  Google Scholar 

  14. Y. Komori, Notes on singular integrals on some inhomogeneous Herzsp aces. Taiwanese J. Math. 8 (2004), 547–556.

    MathSciNet  MATH  Google Scholar 

  15. Y. Komori-Furuya and K. Matsuoka, Strong and weak estimates for fractional integral operators on some Herz-type function spaces. Proceedings of the Maratea Conference FAAT 2009, Rendiconti del Circolo Mathematico di Palermo, Serie II, Suppl., 82 (2010), 375–385.

    Google Scholar 

  16. Y. Komori-Furuya, K. Matsuoka, E. Nakai and Y. Sawano, Integral operators on Bσ-Morrey–Campanato spaces. Rev. Mat. Complut. 26 (2013) 1–32, DOI:10.1007/ s13163-011-0091-6.

    Article  MathSciNet  MATH  Google Scholar 

  17. S.Z. Lu and D.C. Yang, The Littlewood–Paley function and ϕ-transform characterizations of a new Hardy space HK2 associated with the Herzsp ace. Studia Math. 101 (1992), no. 3, 285–298.

    MathSciNet  MATH  Google Scholar 

  18. S.Z. Lu and D.C. Yang, The central BMO spaces and Littlewood–Paley operators. Approx. Theory Appl. 11 (1995), 72–94.

    MathSciNet  MATH  Google Scholar 

  19. K. Matsuoka and E. Nakai, Fractional integral operators on Bp, with Morrey– Campanato norms. Function Spaces IX, Banach Center Publ. 92, 249–264, Inst. Math., Polish Acad. Sci., Warsawa, 2011.

    Google Scholar 

  20. T. Mizuhara, Relations between Morrey and Campanato spaces with some growth functions, II. Proceedings of Harmonic Analysis Seminar 11, pp. 67–74 (1995) (in Japanese).

    Google Scholar 

  21. E. Nakai, Hardy–Littlewood maximal operator, singular integral operators and the Rieszp otentials on generalized Morrey spaces. Math. Nachr. 166 (1994), 95–103.

    Article  MathSciNet  MATH  Google Scholar 

  22. E. Nakai, The Campanato, Morrey and H¨older spaces on spaces of homogeneous type. Studia Math. 176 (2006), no. 1, 1–19.

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Peetre, On convolution operators leaving Lp, spaces invariant. Ann. Math. Pure Appl. 72 (1966), 295–304.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Economics, Nihon University, 1-3-2 Misaki-cho, Chiyoda-ku Tokyo, 101-8360, Japan

    Katsuo Matsuoka

Authors
  1. Katsuo Matsuoka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Katsuo Matsuoka .

Editor information

Editors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Manuel Cepedello Boiso

  2. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    Håkan Hedenmalm

  3. Department of Mathematics & Computer Sci, Free University Amsterdam, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Alfonso Montes Rodríguez

  5. Department of Mathematics, Brown University, Providence, Rhode Island, USA

    Sergei Treil

Additional information

Dedicated to Professor Akihiko Miyachi in celebration of his 60th birthday.

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Basel

About this paper

Cite this paper

Matsuoka, K. (2014). B σ-Campanato Estimates for Commutators of Calderón–Zygmund Operators. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_22

Download citation

Publish with us

Policies and ethics

Search

Navigation