Abstract
The function spaces D k ( R n ) are introduced and studied. The definition of these spaces is based on a regularity property for the critical Sobolev spaces W s , p ( R n ) , where s p = n , obtained by J. Bourgain, H. Brezis, New estimates for the Laplacian, the div–curl, and related Hodge systems, C. R. Math. Acad. Sci. Paris 338 (7) (2004) 539–543 (see also J. Van Schaftingen, Estimates for L 1-vector fields, C. R. Math. Acad. Sci. Paris 339 (3) (2004) 181–186). The spaces D k ( R n ) contain all the critical Sobolev spaces. They are embedded in BMO ( R n ) , but not in VMO ( R n ) . Moreover, they have some extension and trace properties that BMO ( R n ) does not have.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.