An embedding theorem for Campanato spaces

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