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On improved Hardy-type inequalities in Log-Weighted Sobolev Spaces

  • Sourav Ghosh
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Abstract

We prove sharp Hardy-type inequalities in Log-weighted Sobolev spaces. Due to the non-attainability of the sharp constant, we improve these inequalities by adding suitable remainder terms consisting of optimal weights and sharp constants. Consequently, this gives an infinite series improvement in Log-weighted Sobolev spaces. Next, by using these improved Hardy-type inequalities, we also prove an optimal Leray-Trudinger-type improvement. Furthermore, we derive interpolation between Hardy-type inequalities and Leray-Trudinger-type inequalities.

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Cite

BibTeXRIS
BibTeX
@misc{ghosh2026improved,
  title = {{On improved Hardy-type inequalities in Log-Weighted Sobolev Spaces}},
  author = {Sourav Ghosh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03668},
  eprint = {2610.03668},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03668},
}
RIS
TY  - UNPB
TI  - On improved Hardy-type inequalities in Log-Weighted Sobolev Spaces
AU  - Sourav Ghosh
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03668
UR  - https://arxiv.org/abs/2610.03668
AB  - We prove sharp Hardy-type inequalities in Log-weighted Sobolev spaces. Due to the non-attainability of the sharp constant, we improve these inequalities by adding suitable remainder terms consisting of optimal weights and sharp constants. Consequently, this gives an infinite series improvement in Log-weighted Sobolev spaces. Next, by using these improved Hardy-type inequalities, we also prove an optimal Leray-Trudinger-type improvement. Furthermore, we derive interpolation between Hardy-type inequalities and Leray-Trudinger-type inequalities.
ER  -