# name
Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms

# metadata.dc.description.abstract[].value
This paper deals with the behavior of the periodic Gagliardo seminorm under two
types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric
decreasing rearrangement. Our two main results are Pólya-Szegó type inequalities for these
rearrangements. We also deal with the cases of equality.
Our method uses, among others, some classical nonexpansivity results for rearrangements
for which we provide some slight improvements. Our proof is based on the ideas of [Frank
and Seiringer, Non-linear ground state representations and sharp Hardy inequalities, J. Funct.
Anal., 2008], where a new proof to deal with the cases of equality in the nonexpansivity theorem
was given, albeit in a special case involving the rearrangement of only one function.

# metadata.dc.relation.ispartof[].value
Transactions of the American Mathematical Society, 2025, vol. 378, p. 7163-7197

# metadata.dc.rights[].value
cc-by-nc-nd (c) American Mathematical Society (AMS), 2025

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms