An Embedding Theorem for Campanato Spaces

Abstract

The purpose of this paper is to give a Sobolev type embedding theorem for the spaces Lλ,sp,q (ℝn). The homogeneous versions of these spaces contain well known spaces such as the Bounded Mean Oscillation spaces (BMO) and the Campanato spaces L2,λ. Our result extends some injections obtained by Campanato [3, 4], Strichartz [11], and Stein and Zygmund [10].