Decompositions for local Morrey spaces

Abstract

We develop and apply a decomposition theory for generic local Morrey spaces. Our results are smooth and nonsmooth decompositions, which follows from the fact that local Morrey spaces are isomorphic to local Hardy-Morrey spaces and local Triebel-Lizorkin-Morrey spaces in the generic case. As an application of our results, we consider a bilinear estimate for the fractional integral operators.