Endpoint Schatten class properties of commutators
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914800011837440 |
|---|---|
| author | Frank, Rupert L. Sukochev, Fedor Zanin, Dmitriy |
| author_facet | Frank, Rupert L. Sukochev, Fedor Zanin, Dmitriy |
| contents | We study trace ideal properties of the commutators $[(-Δ)^{\fracε{2}},M_f]$ of a power of the Laplacian with the multiplication operator by a function $f$ on $\mathbb R^d$. For a certain range of $ε\in\mathbb R$, we show that this commutator belongs to the weak Schatten class $\mathcal L_{\frac d{1-ε},\infty}$ if and only if the distributional gradient of $f$ belongs to $L_{\frac d{1-ε}}$. Moreover, in this case we determine the asymptotics of the singular values. Our proofs use, among other things, the tool of Double Operator Integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Endpoint Schatten class properties of commutators Frank, Rupert L. Sukochev, Fedor Zanin, Dmitriy Functional Analysis Analysis of PDEs Operator Algebras Spectral Theory We study trace ideal properties of the commutators $[(-Δ)^{\fracε{2}},M_f]$ of a power of the Laplacian with the multiplication operator by a function $f$ on $\mathbb R^d$. For a certain range of $ε\in\mathbb R$, we show that this commutator belongs to the weak Schatten class $\mathcal L_{\frac d{1-ε},\infty}$ if and only if the distributional gradient of $f$ belongs to $L_{\frac d{1-ε}}$. Moreover, in this case we determine the asymptotics of the singular values. Our proofs use, among other things, the tool of Double Operator Integrals. |
| title | Endpoint Schatten class properties of commutators |
| topic | Functional Analysis Analysis of PDEs Operator Algebras Spectral Theory |
| url | https://arxiv.org/abs/2405.10652 |