TY - JOUR
T1 - Variable Besov Spaces: Continuous Version
AU - Drihem , Douadi
JO - Journal of Mathematical Study
VL - 2
SP - 178
EP - 226
PY - 2019
DA - 2019/05
SN - 52
DO - http://doi.org/10.4208/jms.v52n2.19.05
UR - https://global-sci.org/intro/article_detail/jms/13158.html
KW - Atom, embeddings, Besov space, variable exponent.
AB - <p style="text-align: justify;">We introduce Besov spaces with variable smoothness and integrability by
using 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 characterize
these function spaces by so-called Peetre maximal functions and we obtain the Sobolev
embeddings for these function spaces. We use these results to prove the atomic decomposition for these spaces.</p>