Some Analytical Properties of Multivariate Fractal Functions in Lebesgue Spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916679258210304 |
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| author | Rani, Kiran Lal, Rattan |
| author_facet | Rani, Kiran Lal, Rattan |
| contents | In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to Lebesgue spaces. Then, we give analytical properties of the defined fractal operator in Lebesgue spaces. We end this article by showing the existence of Schauder basis of the associated fractal functions for the space $\mathcal{L}^q(I^n, μ_p)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Analytical Properties of Multivariate Fractal Functions in Lebesgue Spaces Rani, Kiran Lal, Rattan Functional Analysis 28A80 In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to Lebesgue spaces. Then, we give analytical properties of the defined fractal operator in Lebesgue spaces. We end this article by showing the existence of Schauder basis of the associated fractal functions for the space $\mathcal{L}^q(I^n, μ_p)$. |
| title | Some Analytical Properties of Multivariate Fractal Functions in Lebesgue Spaces |
| topic | Functional Analysis 28A80 |
| url | https://arxiv.org/abs/2504.06117 |