Skip to main content
Log in

A characterization of the Morrey-Campanato spaces

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

Abstract.

In this paper, we give a new characterization of the Morrey–Campanato spaces by using the convolution φ t B *f(x) to replace the minimizing polynomial P B f of a function f in the Morrey-Campanato norm, where is an appropriate Schwartz function.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bui, H.Q., Taibleson, M.H.: The characterization of the Triebel-Lizorkin spaces for p=∞. J. Fourier Anal. Appl. 6, 537–550 (2000)

    Google Scholar 

  2. Campanato, S.: Proprietà di una famiglia di spazi funzionali. Ann Scuola Norm. Sup. Pisa (3). 18, 137–160 (1964)

    Google Scholar 

  3. Duong, X.T., Yan, L.X.: New function spaces of BMO type, the John-Nirenberg inequality, interpolation and applications. to appear in Comm. Pure Appl. Math., 2004

  4. Fefferman, C., Stein, E.M.: Hp spaces of several variables. Acta Math. 129, 137–195 (1972)

    Google Scholar 

  5. Greenwald, H.: On the theory of homogeneous Lipschitz spaces and Campanato spaces. Pacific J. Math. 106, 87–93 (1983)

    Google Scholar 

  6. Journé, J.L.: Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón. Lecture Notes in Math. 994, Springer, Berlin, 1983

  7. John, F., Nirenberg, L.: On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14, 415–426 (1961)

    Google Scholar 

  8. Janson, S., Taibleson, M.H., Weiss, G.: Elementary characterizations of the Morrey-Campanato spaces. Lecture Notes in Math. 992, 101–114 (1983)

    Google Scholar 

  9. Martell, J.M.: Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications. Studia Math. 161, 113–145 (2004)

    Google Scholar 

  10. Morrey, C.B.: Partial regularity results for non-linear elliptic systems. J. Math. Mech. 17, 649–670 (1967/1968)

    Google Scholar 

  11. Peetre, J.: On the theory of spaces. J. Funct. Analysis 4, 71–87 (1969)

    Google Scholar 

  12. Ricci, F., Taibleson, M.H.: Boundary values of harmonic functions in mixed norm spaces and their atomic structure. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4). 10, 1–54 (1983)

    Google Scholar 

  13. Taibleson, M.H., Weiss, G.: The molecular characterization of certain Hardy spaces. Astérisque. 77, 68–149 (1980)

    Google Scholar 

  14. Yosida, K.: Functional Analysis (5 edn). Springer, Berlin Heidelberg, 1978

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xuan Thinh Duong.

Additional information

D.G. Deng and L.X. Yan are partially supported by NSF of China and the Foundation of Advanced Research Center, Zhongshan University. X.T. Duong and L.X. Yan are supported by a Discovery grant from Australia Research Council.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deng, D., Duong, X. & Yan, L. A characterization of the Morrey-Campanato spaces. Math. Z. 250, 641–655 (2005). https://doi.org/10.1007/s00209-005-0769-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-005-0769-x

Mathematics Subject Classification (2000):

Navigation