Annali dell’Università di Ferrara

, Volume 24, Issue 1, pp 89–98 | Cite as

Anisotropic sobolev theorems

  • Umberto Neri


The purpose of this note is twofold: to present a simple proof of a modern Sobolev theorem (cf. Theorem 1 below) and to discuss a natural generalization of the same in the context of certain Morrey spaces.


Morrey Space Isotropic Dilation Nest Family Usual Lebesgue Space Convolution Inequality 
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.


Lo scopo di questa nota è duplice: presentare una semplice dimostrazione di un moderno teorema di Sobolev (cfr. Teorema 1) e discutere una naturale generalizzazione di tale teorema nel contesto di certi spazi di Morrey.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. R. Adams,A trace inequality for generalized potentials, Studia Math.,48 (1973), pp. 99–105.MathSciNetGoogle Scholar
  2. [2]
    D. R. Adams,A note on Riesz Potentials, Duke Math. J.,42 (1975), pp. 765–778.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    A. P. CalderónA. Torchinsky,Parabolic maximal functions associated with a distribution, I, Advances in Math.,16 (1975), pp. 1–64.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    L. I. Hedberg,On certain convolution inequalities, Proc. Am. Math. Soc.,36 (1972), pp. 505–510.CrossRefMathSciNetGoogle Scholar
  5. [5]
    R. Johnson—U. Neri,Remarks on Riesz potential BMO and Lip (α, P)spaces, Univ. of Md., TR-76-25 (1976).Google Scholar
  6. [6]
    J. Peetre,On the theory of L p, λ spaces, J. Funct. Analysis,4 (1969), pp. 71–87.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    N. M. Rivière,Singular integrals and multiplier operators, Ark. för Mat.,9 (1971), pp. 243–278.MATHCrossRefGoogle Scholar
  8. [8]
    N. M. Rivière,Interpolaciön a la Marcinkiewicz, Rev. Un. Mat. Argentina,25, (1971), pp. 363–377.MATHGoogle Scholar
  9. [9]
    A. Torchinsky,On a mean value inequality, Bull. Am. Math. Soc.,81 (1975), pp. 950–953.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Università degli Studi di Ferrara 1978

Authors and Affiliations

  • Umberto Neri
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege Park

Personalised recommendations