Variable Besov Spaces: Continuous Version (Journal of Mathematical Study, 2019)
We introduce Besov spaces with variable smoothness and integrability byusing the continuous version of Calderón reproducing formula. We show that our space is well-defined, i.e., independent of the choice of basis functions. We characterizethese function spaces by so-called Peetre maximal functions and we obtain the Sobolevembeddings for these function spaces. We use these results to prove the atomic decomposition for these spaces.
Keywords: Atom; embeddings; Besov space; variable exponent.