Submitted Paper
Inserted: 25 sep 2026
Last Updated: 25 sep 2026
Year: 2026
Abstract:
We prove that the Pólya-Szegő inequality for the $L^p$ norm of the Riesz fractional $s$-gradient fails for every $p\in[1,2)$ and $s\in(0,1)$, thus providing a negative answer to a question posed by Nguyen and Squassina in 2017.
Keywords: Fractional Gradient, fractional variation, Riesz potential, symmetric decreasing rearrangement, Pólya-Szegő inequality
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