Divergent Fourier Series with Respect to Biorthonormal Systems in Function Spaces Near $L^1$
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914287163801600 |
|---|---|
| author | Devdariani, Nikoloz |
| author_facet | Devdariani, Nikoloz |
| contents | In this paper, we generalize Bochkarev's theorem, which states that for any uniformly bounded biorthonormal system $Φ$, there exists a Lebesgue integrable function whose Fourier series with respect to the system $Φ$ diverges on a set of positive measure. We find the class of variable exponent Lebesgue spaces $L^{p(\cdot)}([0,1]^n)$, where $1 < p(x) < \infty$ almost everywhere on $[0,1]^n$, such that the aforementioned Bochkarev's theorem holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20685 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Divergent Fourier Series with Respect to Biorthonormal Systems in Function Spaces Near $L^1$ Devdariani, Nikoloz Functional Analysis 46E30, 42A16, 42A20 In this paper, we generalize Bochkarev's theorem, which states that for any uniformly bounded biorthonormal system $Φ$, there exists a Lebesgue integrable function whose Fourier series with respect to the system $Φ$ diverges on a set of positive measure. We find the class of variable exponent Lebesgue spaces $L^{p(\cdot)}([0,1]^n)$, where $1 < p(x) < \infty$ almost everywhere on $[0,1]^n$, such that the aforementioned Bochkarev's theorem holds. |
| title | Divergent Fourier Series with Respect to Biorthonormal Systems in Function Spaces Near $L^1$ |
| topic | Functional Analysis 46E30, 42A16, 42A20 |
| url | https://arxiv.org/abs/2601.20685 |