The first purpose of this paper is to set up several enhancements of the Hardy type inequalities on certain subspaces of the Sobolev spaces. The second aim is to explore the role of the spherical derivative in such improvements and to prove some weighted versions of the Hardy inequality with spherical derivative. As applications of our results, we establish several Hardy’s inequalities and the Hardy inequalities with spherical derivatives on half-spaces.

中文翻译：

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具有球形导数的改进的Hardy不等式和加权Hardy型不等式

本文的首要目的是在Sobolev空间的某些子空间上建立Hardy型不等式的几种增强。第二个目的是探索球形导数在此类改进中的作用，并证明带有球形导数的Hardy不等式的一些加权形式。作为我们结果的应用，我们在半空间上建立了球状导数的几个Hardy不等式和Hardy不等式。