@article{Gao2025, 
author = {Tian Gao and Dan Ma},
title = {The        L    p  -Petty projection inequality for    s-concave functions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {7706-7716},
keywords = {s-concave function, Lp-projection body, Lp-Petty projection inequality, Lp isoperimetric inequality},
url = {https://www.sciopen.com/article/10.3934/math.2025353},
doi = {10.3934/math.2025353},
abstract = {We study the "functionalization" of the        L    p  -projection body and two related important inequalities in geometry. On the class of    s-concave functions, a general function counterpart of the        L    p  -projection body is introduced. In addition, the        L    p  -Petty projection inequality and the        L    p   isoperimetric inequality are established on this class. Finally, we show that the        L    p  -Petty projection inequality strengthens the        L    p   isoperimetric inequality on the same class.}
}