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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.08039 |
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| _version_ | 1866912067753082880 |
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| author | Kassymov, Aidyn Ruzhansky, Michael Suragan, Durvudkhan |
| author_facet | Kassymov, Aidyn Ruzhansky, Michael Suragan, Durvudkhan |
| contents | In this paper, we obtain a fractional Hardy inequality in the case $Q<sp$ on homogeneous Lie groups, and as an application we show the corresponding uncertainty principle. Also, we show a fractional Hardy-Sobolev type inequality on homogeneous Lie groups. In addition, we prove fractional logarithmic Hardy-Sobolev and fractional Nash type inequalities on homogeneous Lie groups. We note that the case $Q>sp$ was extensively studied in the literature, while here we are dealing with the complementary range $Q<sp$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08039 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Hardy type inequalities on homogeneous Lie groups in the case $Q<sp$ Kassymov, Aidyn Ruzhansky, Michael Suragan, Durvudkhan Analysis of PDEs In this paper, we obtain a fractional Hardy inequality in the case $Q<sp$ on homogeneous Lie groups, and as an application we show the corresponding uncertainty principle. Also, we show a fractional Hardy-Sobolev type inequality on homogeneous Lie groups. In addition, we prove fractional logarithmic Hardy-Sobolev and fractional Nash type inequalities on homogeneous Lie groups. We note that the case $Q>sp$ was extensively studied in the literature, while here we are dealing with the complementary range $Q<sp$. |
| title | Fractional Hardy type inequalities on homogeneous Lie groups in the case $Q<sp$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.08039 |