Sharp inequalities of the parameterized functional \(U_j\) for Borel measures on the unit sphere in \({\mathbb {R}}^n\) are established. As two applications, some inequalities related to cone-volume measures and Schneider’s projection problem are obtained.

中文翻译：

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与函数$$ U_j $$ U j和某些应用有关的尖锐不等式

建立了参数化函数\（U_j \）在\（{\ mathbb {R}} ^ n \）中单位球面上Borel测度的尖锐不等式。作为两个应用，获得了一些与锥量测度和施耐德投影问题有关的不等式。