Vector valued Hardy spaces related to analytic functions having distributional boundary values
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2018
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| Acceso en línea: | |
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| _version_ | 1866911919315615744 |
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| author | Carmichael, Richard D. Pilipović, Stevan Vindas, Jasson |
| author_facet | Carmichael, Richard D. Pilipović, Stevan Vindas, Jasson |
| contents | The Hardy space $H^{p}$ of vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ with values in Hilbert space and which have vector valued tempered distributions as boundary value are proved to be in $H^{p}$ corresponding to Hilbert space if the boundary value is in $L^{p}$ with values in Hilbert space. A Poisson integral representation for such vector valued analytic functions is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_06709 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Vector valued Hardy spaces related to analytic functions having distributional boundary values Carmichael, Richard D. Pilipović, Stevan Vindas, Jasson Functional Analysis Primary 32A07, 32A35, 46F05, 46F20, Secondary 32A26 The Hardy space $H^{p}$ of vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ with values in Hilbert space and which have vector valued tempered distributions as boundary value are proved to be in $H^{p}$ corresponding to Hilbert space if the boundary value is in $L^{p}$ with values in Hilbert space. A Poisson integral representation for such vector valued analytic functions is obtained. |
| title | Vector valued Hardy spaces related to analytic functions having distributional boundary values |
| topic | Functional Analysis Primary 32A07, 32A35, 46F05, 46F20, Secondary 32A26 |
| url | https://arxiv.org/abs/1801.06709 |