@article{Guo2026, 
author = {Wentao Guo and Yuke Li and Xiaolin Zeng},
title = {A generalization of affine fractional        L    p   Sobolev inequalities},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {22959-22982},
keywords = {fractional Sobolev inequality, fractional Lp polar projection body, symmetric decreasing rearrangement, Pólya–Szegö inequality},
url = {https://www.sciopen.com/article/10.3934/math.2026925},
doi = {10.3934/math.2026925},
abstract = {General affine fractional        L    p   Sobolev inequalities were established by  Monika Ludwig and Julián Haddad in their foundational work for fractional parameters    s  ∈  (  0  ,  1  ) and    1  <  p  <  n      /    s. In this paper, we extend the admissible range of the fractional parameter to    s  ∈  (  0  ,  n  )  ∖      N   and    1  <  p  <  n      /    s. The affine fractional        L    p   Sobolev inequalities are obtained for both the classical fractional case    s  ∈  (  0  ,  1  ) and the higher-order fractional case. In the course of the proof, we define the higher-order fractional        L    p   Sobolev polar projection body and use the method of symmetric decreasing rearrangement.}
}