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arXiv · 2407.15197

On fractional inequalities on metric measure spaces with polar decomposition

Aidyn Kassymov·Michael Ruzhansky·Gulnur Zaur
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Abstract

In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for $1<p\leq q<\infty$ is playing a key role in the proof. Moreover, we also prove the fractional Hardy-Sobolev type inequality on metric measure spaces. In addition, logarithmic Hardy-Sobolev and fractional Nash type inequalities on metric measure spaces are presented. In addition, we present applications on homogeneous groups and on the Heisenberg group.

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Aidyn Kassymov, Michael Ruzhansky, Gulnur Zaur. 2024-07-21. On fractional inequalities on metric measure spaces with polar decomposition. https://arxiv.org/abs/2407.15197

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