Decomposition and characterization of VMO via vanishing Carleson measures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915868647096320 |
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| author | Tao, Fei Yang, Yaosong |
| author_facet | Tao, Fei Yang, Yaosong |
| contents | We establish two equivalent characterizations of $\mathrm{VMO}$ in terms of vanishing Carleson measures. First, we show that any $\mathrm{VMO}$ function admits a decomposition into a continuous boundary term and an integral operator associated with a vanishing Carleson measure. Second, motivated by Varopoulos's work on the $\bar{\partial}$-equation, we characterize $\mathrm{VMO}$ via the boundary values of smooth functions whose gradients induce vanishing Carleson measures.
As a consequence, we recover the known representation \[ \mathrm{VMO}=\mathrm{VLO}-\mathrm{VLO}, \] thereby providing a new perspective on this decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06155 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decomposition and characterization of VMO via vanishing Carleson measures Tao, Fei Yang, Yaosong Complex Variables 30H35, 30H05, 42B35, 30J99 We establish two equivalent characterizations of $\mathrm{VMO}$ in terms of vanishing Carleson measures. First, we show that any $\mathrm{VMO}$ function admits a decomposition into a continuous boundary term and an integral operator associated with a vanishing Carleson measure. Second, motivated by Varopoulos's work on the $\bar{\partial}$-equation, we characterize $\mathrm{VMO}$ via the boundary values of smooth functions whose gradients induce vanishing Carleson measures. As a consequence, we recover the known representation \[ \mathrm{VMO}=\mathrm{VLO}-\mathrm{VLO}, \] thereby providing a new perspective on this decomposition. |
| title | Decomposition and characterization of VMO via vanishing Carleson measures |
| topic | Complex Variables 30H35, 30H05, 42B35, 30J99 |
| url | https://arxiv.org/abs/2309.06155 |