星体的对偶Orlicz Hausdorff度量和对偶混合亮度积分

发布时间：2018-09-14 07:02

【摘要】：本文以星体的对偶Orlicz Hausdorff度量的刻画问题和星体的对偶混合亮度积分及其极值问题为主要研究对象。我们引进了星体的对偶Orlicz Hausdorff度量的概念,并将其与经典的对偶Hausdorff度量和对偶1Hausdorff度量进行了比较。进而讨论了这一新度量的一些基本性质。这一度量为计算Orlicz空间中星体之间的距离提供了便利。我们还对星体引进了对偶混合亮度积分的概念,进而研究了其相关极值问题,建立了对不同指数的循环不等式,以及它与星体的截面体体积之间的重要联系。
[Abstract]:In this paper, we focus on the characterization of dual Orlicz Hausdorff metric of stars and the dual mixed luminance integral and its extremum of stars. We introduce the concept of dual Orlicz Hausdorff metric of stars and compare it with the classical dual Hausdorff metric and dual 1Hausdorff metric. Then some basic properties of this new metric are discussed. This metric facilitates the calculation of distances between stars in Orlicz space. We also introduce the concept of dual mixed luminance integral to the star, and then study its correlation extremum problem, establish the cyclic inequality for different exponents and the important relation between it and the volume of the cross section body of the star.
【学位授予单位】：重庆师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O186.5

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