关于 $$p$$ - 质点积分的一些不等式

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI:10.1134/S0016266323020028

Weidong Wang, Yanping Zhou

引用次数: 0

摘要

Abstract 在本文中，我们将质点积分、调和质点积分和仿射质点积分的概念推广到了$p$-质点积分，从而使$p$-质点积分的$p=1, -1, -n$情况分别是质点积分、调和质点积分和仿射质点积分。此外，我们还得到了一些与 $p$-quermassintegrals 相关的不等式，包括 $L_q$ Brunn-Minkowski 型不等式、单调不等式和 Bourgain-Milman 型不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some Inequalities for $p$-Quermassintegrals

In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to $p$-quermassintegrals so that the cases $p=1, -1, -n$ of $p$-quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with $p$-quermassintegrals, including $L_q$ Brunn–Minkowski-type inequalities, a monotonic inequality, and a Bourgain–Milman-type inequality.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.