Volume 52, Issue 2
Variable Besov Spaces: Continuous Version

Douadi Drihem

J. Math. Study, 52 (2019), pp. 178-226.

Published online: 2019-05

Preview Full PDF 442 7595
Export citation
  • 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.

  • Keywords

Atom, embeddings, Besov space, variable exponent.

  • AMS Subject Headings

46E35, 46E30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

douadidr@yahoo.fr (Douadi Drihem)

  • BibTex
  • RIS
  • TXT
@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} }
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 -

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.

Douadi Drihem. (2019). Variable Besov Spaces: Continuous Version. Journal of Mathematical Study. 52 (2). 178-226. doi:10.4208/jms.v52n2.19.05
Copy to clipboard
The citation has been copied to your clipboard