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Failure of the Pólya-Szegő inequality for the fractional gradient
Abstract
We prove that the Pólya-Szegő inequality for the Lp norm of the Riesz fractional s-gradient fails for every p∈[1,2) and s∈(0,1), thus providing a negative answer to a question posed by Nguyen and Squassina in 2017.
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BibTeX
@misc{stefani2026failure,
title = {{Failure of the Pólya-Szegő inequality for the fractional gradient}},
author = {Giorgio Stefani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31233},
eprint = {2609.31233},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31233},
}
RIS
TY - UNPB
TI - Failure of the Pólya-Szegő inequality for the fractional gradient
AU - Giorgio Stefani
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31233
UR - https://arxiv.org/abs/2609.31233
AB - We prove that the Pólya-Szegő inequality for the L^p norm of the Riesz fractional s-gradient fails for every p∈[1,2) and s∈(0,1), thus providing a negative answer to a question posed by Nguyen and Squassina in 2017.
ER -