Electron. J. Diff. Eqns., Vol. 2002(2002), No. 66, pp. 1-18.

An embedding theorem for Campanato spaces

Azzeddine El Baraka

The purpose of this paper is to give a Sobolev type embedding theorem for the spaces ${\cal L}_{p,q}^{\lambda,s}(\mathbb{R}^{n})$. The homogeneous versions of these spaces contain well known spaces such as the Bounded Mean Oscillation spaces (BMO) and the Campanato spaces ${\cal L}^{2,\lambda}$. Our result extends some injections obtained by Campanato [3,4], Strichartz [11], and Stein and Zygmund [10].

Submitted April 15, 2002. Published July 11, 2002.
Math Subject Classifications: 46E35.
Key Words: Sobolev embeddings, BMO, Campanato spaces.

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Azzeddine El Baraka
Universite Mohamed Ben Abdellah, FST Fes-Saiss
Departement de Mathematiques
BP2202, Route Immouzer
Fes 30000 Morocco
e-mail: aelbaraka@yahoo.com

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