Mathematische Zeitschrift

, Volume 250, Issue 3, pp 641–655 | Cite as

A characterization of the Morrey-Campanato spaces



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 Open image in new window is an appropriate Schwartz function.

Mathematics Subject Classification (2000):

42B35 47G10 


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  1. 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. 2.
    Campanato, S.: Proprietà di una famiglia di spazi funzionali. Ann Scuola Norm. Sup. Pisa (3). 18, 137–160 (1964)Google Scholar
  3. 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., 2004Google Scholar
  4. 4.
    Fefferman, C., Stein, E.M.: Hp spaces of several variables. Acta Math. 129, 137–195 (1972)Google Scholar
  5. 5.
    Greenwald, H.: On the theory of homogeneous Lipschitz spaces and Campanato spaces. Pacific J. Math. 106, 87–93 (1983)Google Scholar
  6. 6.
    Journé, J.L.: Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón. Lecture Notes in Math. 994, Springer, Berlin, 1983Google Scholar
  7. 7.
    John, F., Nirenberg, L.: On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14, 415–426 (1961)Google Scholar
  8. 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. 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. 10.
    Morrey, C.B.: Partial regularity results for non-linear elliptic systems. J. Math. Mech. 17, 649–670 (1967/1968)Google Scholar
  11. 11.
    Peetre, J.: On the theory of Open image in new window spaces. J. Funct. Analysis 4, 71–87 (1969)Google Scholar
  12. 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. 13.
    Taibleson, M.H., Weiss, G.: The molecular characterization of certain Hardy spaces. Astérisque. 77, 68–149 (1980)Google Scholar
  14. 14.
    Yosida, K.: Functional Analysis (5 edn). Springer, Berlin Heidelberg, 1978Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsZhongshan UniversityGuangzhouP.R. China
  2. 2.Department of MathematicsMacquarie UniversityAustralia

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