| Abstrakt: |
Abstract: 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. |
Full text from SpringerLink