Interpolation and duality of generalized grand Morrey spaces on quasi-metric measure spaces

Title:

Interpolation and duality of generalized grand Morrey spaces on quasi-metric measure spaces

Creator:

Liu, Yi and Yuan, Wen

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7ef34a40-637c-4500-8008-f3aa30bcc335
uuid:7ef34a40-637c-4500-8008-f3aa30bcc335
issn:0011-4642

Subject:

matematika, mathematics, grand Lebesgue space, grand Morrey space, Gagliardo-Peetre method, Calderón product, predual space, $\pm$ interpolation method, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

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., Yi Liu, Wen Yuan., and Obsahuje bibliografické odkazy

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

715-732

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:3

Harvested from:

CDK

Metadata only:

false