Higher <i>P</i>-symmetric Ekeland-Hofer capacities

This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for \begin{document}$ P $\end{document} -symmetric subsets in the standard symplectic space \begin{document}$ (\mathbb{R}^{2n},\omega_0) $\end{document} , which is motivated by Long and Dong's study about \begin{document}$ P $\end{document} -symmetric closed characteristics on \begin{document}$ P $\end{document} -symmetric convex bodies. We study the relationship between these capacities and other capacities, and give some computation examples. Moreover, we also define higher real symmetric Ekeland-Hofer capacities as a complement of Jin and the second named author's recent study of the real symmetric analogue about the first Ekeland-Hofer capacity.