Multipliers for local Morrey spaces

An exact description of the multiplier space between two local Morrey spaces is found. It is shown that, under natural restrictions, the multiplier space for a couple of local Morrey spaces is an approximation local Morrey space, which is constructed systematically from the original spaces. An example is given showing that, in this case, the approximation local Morrey space cannot be replaced by a local Morrey space.