Nonexistence of Henkin type projections via a Wiener theorem for multipliers
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913061982437376 |
|---|---|
| author | Curcă, Eduard Wojciechowski, Michał |
| author_facet | Curcă, Eduard Wojciechowski, Michał |
| contents | Let $d\geq 2$, $l\geq 0$ and suppose $X$ is one of the function spaces $W^{l,1}(\mathbb{T}^{d})$, $W^{l,\infty }(\mathbb{T}^{d})$ or $C^{l}(\mathbb{T}^{d})$. We extend a result of Henkin (1967), showing that, for appropriate $N\times N$ matrix operators $A(D)$, the subspace of $X^{N}$ consisting of $A(D)-$free elements is noncomplemented. In order to prove this we establish a new property of the Fourier multipliers that are bounded on $X$: the kernel $k$ of any such multiplier obeys a weaker version of Wiener's theorem for the singularities of measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23161 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonexistence of Henkin type projections via a Wiener theorem for multipliers Curcă, Eduard Wojciechowski, Michał Functional Analysis 42B15, 42B05, 46E35 Let $d\geq 2$, $l\geq 0$ and suppose $X$ is one of the function spaces $W^{l,1}(\mathbb{T}^{d})$, $W^{l,\infty }(\mathbb{T}^{d})$ or $C^{l}(\mathbb{T}^{d})$. We extend a result of Henkin (1967), showing that, for appropriate $N\times N$ matrix operators $A(D)$, the subspace of $X^{N}$ consisting of $A(D)-$free elements is noncomplemented. In order to prove this we establish a new property of the Fourier multipliers that are bounded on $X$: the kernel $k$ of any such multiplier obeys a weaker version of Wiener's theorem for the singularities of measures. |
| title | Nonexistence of Henkin type projections via a Wiener theorem for multipliers |
| topic | Functional Analysis 42B15, 42B05, 46E35 |
| url | https://arxiv.org/abs/2604.23161 |