Anisotropic Morrey-type spaces and their interpolation properties

Abstract

In this paper, there are defined the anisotropic local Morrey-type spaces \(LM_{\bar{p},\bar{q}}^{\bar{\lambda}}\) and the anisotropic generalized Morrey-type spaces \(M_{\bar{p},\bar{q}}^{\bar{\lambda}}\), where \(\bar{p}\), \(\bar{q}\), and \(\bar{\lambda}\) are vectors. The spaces \(LM_{\bar{p},\bar{q}}^{\bar{\lambda}}\) allow relaxation of the conditions on the parameter \(\bar{\lambda}\), namely, the components of the given vector can take any real value, i.e., \(-\infty < \lambda_i < \infty,\ i = 1, \overline{d}\), in contrast to previously studied spaces. The embedding properties of the defined spaces are investigated. Additionally, an anisotropic interpolation method is considered, which allows the study of the interpolation properties of these spaces.