Function spaces of BMO and Campanato type

Abstract

To obtain the Littlewood-Paley characterization for Campanato spaces $mathcal{L}^{2,lambda}$ modulo polynomials (which contain as special case the John and Nirenberg space $BMO$), we define and study a scale of function spaces on $mathbb{R}^{n}$. We discuss the real interpolation of these spaces and some embeddings between these spaces and the classical spaces. These embeddings cover some classical results obtained by Campanato, Strichartz, Stein and Zygmund.

Keywords

• BMO-space
• Campanato spaces
• Real interpolation
• Sobolev embeddings.