Abstract
Two scales of harmonic Hardy-Sobolev spaces are introduced and their boundary regularity is studied. Both scales impose conditions on derivatives of harmonic functions in a fixed direction. In one case, they are required to have bounded P-means, while in the other, they are required to have non-tangentialmaximal functions in Lp. The results include embedding in Lipschitz spaces, as well as into spaces of continuous functions and spaces of bounded and vanishing mean oscillation. In particular, real variable versions of the theorem of Privalov on analytic functions with absolutely continuous boundary values are proved.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
