Boundedness of some classical operators on generalized Morrey spaces

  • Takahiro Mizuhara


Let \( \Phi = \Phi (r),r > 0 \), be a growth function, that is, a positive increasing function in \( (0,\infty ) \). Let us assume that the growth function Φ satisfies a doubling condition with a doubling constant D=D(Φ) ≥ 1, that is,
$$ \Phi (2r)D\Phi (r){\text{ for all }}r > 0 $$


Growth Function Singular Integral Operator Morrey Space Maximal Inequality Riesz Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D.R.Adams, A note on Riesz potentials, Duke Math. J. 42 (1975), 765–778.MathSciNetCrossRefGoogle Scholar
  2. [2]
    S.Campanato, Proprieta di una famiglia di spazi funzionali, Ann. Scuola Norm. Sup. Pisa, 18 (1964), 137–160.Google Scholar
  3. [3]
    F.Chiarenza and M.Frasca, Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat.(7), 7 (1987), 273–279.Google Scholar
  4. [4]
    A.Cordoba and C.L.Fefferman, A weighted norm inequality for singular integrals, Studia Math. 57 (1976), 97–101.MathSciNetGoogle Scholar
  5. [5]
    C.L.Fefferman and E.M.Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107–115.CrossRefGoogle Scholar
  6. [6]
    C.L.Fefferman and E.M.Stein, IP spaces of several variables, Acta Math. 129 (1972), 127–193.Google Scholar
  7. [7]
    J.Garcia-Cuerva and J.L.Rubio de Francia, Weighted norm inequalities and related topics, North-Holland, 1985.Google Scholar
  8. [8]
    S.Janson, M.II.Taiblesom and G.Weiss, Elementary characterization of the Morrey- C amp an at o spaces, Proc. in Harmonic Analysis, Cortona, Italy, Springer, Lecture Notes in Math. Vol. 992, 1982, 101–114.Google Scholar
  9. [9]
    R.L.Long, The spaces generated by blocks, Sci. Sinica, Ser.A, 27 (1984), 16–26.Google Scholar
  10. [10]
    C.B.Morrey, Jr. On the solutions of quasi-linear elleptic partial differential equations, Trans. A.M.S. 43 (1938), 126–166.CrossRefGoogle Scholar
  11. [11]
    J.Peetre, On convolution operators leaving LP,X spaces invariant, Aim. Mat. Pur a Appl.(4), 72 (1966), 295–304.CrossRefGoogle Scholar
  12. [12]
    J.Peetre, On the theory of LPX spaces, J. Funct. Anal. 4 (1969), 71–87.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Takahiro Mizuhara
    • 1
  1. 1.Department of MathematicsYamagata UniversityYamagataJapan

Personalised recommendations