On interpolation of local Morrey-type spaces

Abstract

In this paper, we study the interpolation properties of local Morrey-type spaces related to the interpolation method for anisotropic spaces. We define approximation local Morrey spaces \(\overline{LM}_{p,r}^{\lambda,q}\) and approximation spaces \(\widetilde{LM}_{p,r}^{\lambda,q}\), and in terms of these spaces we obtain a description of interpolation spaces for pairs of local Morrey-type spaces \(LM_{p_0,q_0}^{\lambda_0}\), \(LM_{p_1,q_1}^{\lambda_1}\) in the case \(p_0 \neq p_1\).