On Herz-Bochkarev limiting problem
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913885124034560 |
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| author | Nursultanov, Erlan Ghorbanalizadeh, Arash Suragan, Durvudkhan |
| author_facet | Nursultanov, Erlan Ghorbanalizadeh, Arash Suragan, Durvudkhan |
| contents | This paper studies Hausdorff-Young-type inequalities within the framework of Lorentz spaces $L_{p,q}$. Focusing on the dependence of the associated constants on the integrability parameter $p$, we derive optimal bounds in the limiting case $p\rightarrow 2$, addressing the Herz-Bochkarev problem. The results obtained refine the pioneering estimates in [3] and are comparable to recent advances in [16]. The main ingredients of our approach are new grand Lorentz space techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Herz-Bochkarev limiting problem Nursultanov, Erlan Ghorbanalizadeh, Arash Suragan, Durvudkhan Functional Analysis Analysis of PDEs Classical Analysis and ODEs 42A16, 42B35, 46E30 This paper studies Hausdorff-Young-type inequalities within the framework of Lorentz spaces $L_{p,q}$. Focusing on the dependence of the associated constants on the integrability parameter $p$, we derive optimal bounds in the limiting case $p\rightarrow 2$, addressing the Herz-Bochkarev problem. The results obtained refine the pioneering estimates in [3] and are comparable to recent advances in [16]. The main ingredients of our approach are new grand Lorentz space techniques. |
| title | On Herz-Bochkarev limiting problem |
| topic | Functional Analysis Analysis of PDEs Classical Analysis and ODEs 42A16, 42B35, 46E30 |
| url | https://arxiv.org/abs/2506.07478 |