Copyright © 2009 Jiecheng Chen and Hongliang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We investigate the functions spaces on for which the generalized partial derivatives exist and belong to different Lorentz spaces , where and is nonincreasing and satisfies some special conditions. For the functions in these weighted Sobolev-Lorentz spaces, the estimates of the Besov type norms are found. The methods used in the paper are based on some estimates of nonincreasing rearrangements and the application of , weights.