Abstract
Inspired by a recent work of Haddad, Jiménez and Montenegro, we give a new and simple approach to the recently established general affine Pólya–Szegö principle. Our approach is based on the general Lp Busemann–Petty centroid inequality and does not rely on the general Lp Petty projection inequality or the solution of the Lp Minkowski problem. A Brothers–Ziemer-type result for the general affine Pólya–Szegö principle is also established. As applications, we reprove some sharp affine Sobolev-type inequalities and settle their equality conditions. We also prove a stability estimate for the affine Sobolev inequality on functions of bounded variation by using our new approach. As a corollary of this stability result, we deduce a stability estimate for the affine logarithmic-Sobolev inequality.
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.
