Grand Net Spaces and Applications to Integral Operators
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915213698138112 |
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| author | Suragan, Durvudkhan Zaighum, Muhammad Asad |
| author_facet | Suragan, Durvudkhan Zaighum, Muhammad Asad |
| contents | This paper introduces the concept of grand net spaces, a new framework that provides a unified setting for studying various function spaces. Building on the seminal works of [8] and [15], we define grand net spaces and establish their key properties, including embedding results, norm equivalences, and interpolation theorems. We prove that these spaces coincide with grand Lorentz spaces under certain conditions and derive boundedness criteria for integral operators acting on grand net spaces. The latter extends the Nursultanov-Tikhonov theorem established in [16]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_20080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grand Net Spaces and Applications to Integral Operators Suragan, Durvudkhan Zaighum, Muhammad Asad Functional Analysis 42B35, 46E30, 47G10 This paper introduces the concept of grand net spaces, a new framework that provides a unified setting for studying various function spaces. Building on the seminal works of [8] and [15], we define grand net spaces and establish their key properties, including embedding results, norm equivalences, and interpolation theorems. We prove that these spaces coincide with grand Lorentz spaces under certain conditions and derive boundedness criteria for integral operators acting on grand net spaces. The latter extends the Nursultanov-Tikhonov theorem established in [16]. |
| title | Grand Net Spaces and Applications to Integral Operators |
| topic | Functional Analysis 42B35, 46E30, 47G10 |
| url | https://arxiv.org/abs/2503.20080 |