Monotone rearrangement does not increase generalized Campanato norm in VMO
Leonid Slavin, Pavel Zatitskii
TL;DR
This paper proves that monotone rearrangement does not increase the quadratic Campanato-type norm in a quantitative version of the VMO space on an interval.
Contribution
It establishes a new property of monotone rearrangement in the context of a quadratic Campanato-type norm within a quantitative VMO space.
Findings
Monotone rearrangement preserves the quadratic Campanato-type norm.
The result applies to a quantitative version of VMO on an interval.
This extends understanding of rearrangement effects in function spaces.
Abstract
We consider a quantitative version of the space VMO on an interval, equipped with a quadratic Campanato-type norm, and prove that monotone rearrangement does not increase the norm in this space.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Advanced Banach Space Theory · Stability and Controllability of Differential Equations