| Title:
|
Interpolation and duality of generalized grand Morrey spaces on quasi-metric measure spaces (English) |
| Author:
|
Liu, Yi |
| Author:
|
Yuan, Wen |
| Language:
|
English |
| Journal:
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Czechoslovak Mathematical Journal |
| ISSN:
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0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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67 |
| Issue:
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3 |
| Year:
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2017 |
| Pages:
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715-732 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\theta \in (0,1)$, $\lambda \in [0,1)$ and $p,p_0,p_1\in (1,\infty ]$ be such that ${(1-\theta )}/{p_{0}}+{\theta }/{p_{1}}={1}/{p}$, and let $\varphi , \varphi _0, \varphi _1 $ be some admissible functions such that $\varphi , \varphi _0^{{p}/{p_0}}$ and $\varphi _1^{{p}/{p_1}}$ are equivalent. We first prove that, via the $\pm $ interpolation method, the interpolation $\langle L^{p_0),\lambda }_{\varphi _0}(\mathcal {X}), L^{p_1),\lambda }_{\varphi _1}(\mathcal {X}), \theta \rangle $ of two generalized grand Morrey spaces on a quasi-metric measure space $\mathcal {X}$ is the generalized grand Morrey space $L^{p),\lambda }_{\varphi }(\mathcal {X})$. Then, by using block functions, we also find a predual space of the generalized grand Morrey space. These results are new even for generalized grand Lebesgue spaces. (English) |
| Keyword:
|
grand Lebesgue space |
| Keyword:
|
grand Morrey space |
| Keyword:
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Gagliardo-Peetre method |
| Keyword:
|
quasi-metric measure space |
| Keyword:
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Calderón product |
| Keyword:
|
predual space |
| Keyword:
|
$\pm $ interpolation method |
| MSC:
|
46B10 |
| MSC:
|
46B70 |
| idZBL:
|
Zbl 06770125 |
| idMR:
|
MR3697911 |
| DOI:
|
10.21136/CMJ.2017.0081-16 |
| . |
| Date available:
|
2017-09-01T12:22:38Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146854 |
| . |
| Reference:
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