Homogeneous variable exponent Besov and Triebel-Lizorkin spaces - Almeida, Alexandre (2018)
We introduce homogeneous Besov and Triebel--Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.