On parabolic Adams's, the Chiarenza-Frasca theorems, and some other results related to parabolic Morrey spaces

Abstract

We present several results of embedding type for parabolic Morrey and $ L_{p} $ spaces with or without mixed norms. Some other interpolation results for parabolic Morrey spaces are also given. The main object of investigation is the term $ b^{i}D_{i}u $ and the ways to estimate it in various Morrey and $ L_{p} $ spaces in order to be able to treat it as a perturbation term in the parabolic equations.