Vinogradov's three primes theorem in the intersection of multiple Piatetski-Shapiro sets

Vinogradov's three primes theorem indicates that, for every sufficiently large odd integer N, the equation N=p1+p2+p3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=p_1+p_2+p_3$$\end{document} is solvable in prime variables p1,p2,p3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_1,p_2,p_3$$\end{document}. In this paper, it is proved that Vinogradov's three primes theorem still holds with three prime variables constrained in the intersection of multiple Piatetski-Shapiro sequences.