On Hölder continuity and $p^\mathrm{th}$-variation function of Weierstrass-type functions
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| Format: | Preprint |
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2024
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| _version_ | 1866913081326567424 |
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| author | Barczy, Matyas Kern, Peter |
| author_facet | Barczy, Matyas Kern, Peter |
| contents | We study Hölder continuity, $p^\mathrm{th}$-variation function and Riesz variation of Weierstrass-type functions along the sequence of $b$-adic partitions, where $b>1$ is an integer. By a Weierstrass-type function, we mean that in the definition of the well-known Weierstrass function, the power function is replaced by a submultiplicative function, and the Lipschitz continuous cosine and sine functions are replaced by a general periodic Hölder continuous function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_09229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Hölder continuity and $p^\mathrm{th}$-variation function of Weierstrass-type functions Barczy, Matyas Kern, Peter Classical Analysis and ODEs Probability 26A16, 26A45, 60F99 We study Hölder continuity, $p^\mathrm{th}$-variation function and Riesz variation of Weierstrass-type functions along the sequence of $b$-adic partitions, where $b>1$ is an integer. By a Weierstrass-type function, we mean that in the definition of the well-known Weierstrass function, the power function is replaced by a submultiplicative function, and the Lipschitz continuous cosine and sine functions are replaced by a general periodic Hölder continuous function. |
| title | On Hölder continuity and $p^\mathrm{th}$-variation function of Weierstrass-type functions |
| topic | Classical Analysis and ODEs Probability 26A16, 26A45, 60F99 |
| url | https://arxiv.org/abs/2407.09229 |