@Article{JMS-52-178, author = {Drihem , Douadi}, title = {Variable Besov Spaces: Continuous Version}, journal = {Journal of Mathematical Study}, year = {2019}, volume = {52}, number = {2}, pages = {178--226}, abstract = {

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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v52n2.19.05}, url = {http://global-sci.org/intro/article_detail/jms/13158.html} }