Logarithmic Littlewood-Paley Decomposition and Applications to Orlicz Spaces

Abstract

Abstract. This paper is devoted to the construction of a logarithmic Littlewood-Paley decomposition. The approach we adopted to carry out this construction is based on the notion introduced in [9] of being log-oscillating with respect to a scale. The relevance of this theory is illustrated on several examples related to Orlicz spaces.