In this paper, we define an intersection space between weighted classical Lebesgue spaces and weighted Sobolev spaces with variable exponent. We consider the basic properties of the space. Also, we investigate some inclusions, continuous embeddings, and compact embeddings under some conditions.
"Compact embeddings on a subspace of weighted variable exponent Sobolev spaces." Adv. Oper. Theory 4 (2) 388 - 405, Spring 2019. https://doi.org/10.15352/aot.1803-1335