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تسجيل مستخدم جديد$L_p$ John ellipsoids for log-concave functions
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The aim of this paper is to develop the $L_p$ John ellipsoid for the geometry of log-concave functions. Using the results of the $L_p$ Minkowski theory for log-concave function established in cite{fan-xin-ye-geo2020}, we characterize the $L_p$ John ellipsoid for log-concave function, and establish some inequalities of the $L_p$ John ellipsoid for log-concave function. Finally, the analog of Balls volume ratio inequality for the $L_p$ John ellipsoid of log-concave function is established.
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