发表机构
Université Félix Houphouët-Boigny; Université Jean Lorougnon Guédé; Université Nangui Abrogoua（费利克斯·乌弗埃-博瓦尼大学; 让·洛龙·格德大学; 南圭·阿布罗瓜大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究变指数Fofana空间及其预对偶的赋范Köthe结构，确定其Köthe对偶与双对偶，并证明两者均非自反。
AI 中文摘要
Fofana空间是在Wiener amalgam空间基础上引入的，近年来引起了一些关注，并在偏微分方程领域找到了应用。本文研究了变指数Fofana空间$(L^{p(\cdot)}, \ell^{q})^{\alpha}$的预对偶空间$\mathcal{H}(p^{\prime}(\cdot),q^{\prime},\alpha^{\prime})$的赋范Köthe结构，其中$1\leq p(\cdot) \leq \alpha \leq q\leq \infty$。作为这一研究的应用，我们确定了这两个空间的Köthe对偶和Köthe双对偶，并获得了$\mathcal{H}(p^{\prime}(\cdot),q^{\prime},\alpha^{\prime})$的一个预对偶。最后，我们证明了$(L^{p(\cdot)}, \ell^{q})^{\alpha}$和$\mathcal{H}(p^{\prime}(\cdot),q^{\prime},\alpha^{\prime})$都不是自反的。
英文摘要
Fofana spaces, introduced on the basis of Wiener amalgam spaces, have attracted some interest recently and have found applications in the field of partial differential equations. In this paper, we study the normed Köthe structure of the predual spaces $\mathcal{H}(p^{\prime}(\cdot),q^{\prime},α^{\prime})$ of Fofana spaces with variable exponent $(L^{p(\cdot)}, \ell^{q})^α$, where $1\leq p(\cdot) \leq α\leq q\leq \infty$. As an application of this investigation, we identify the Köthe duals and Köthe biduals of these two spaces, and we obtain a predual of $\mathcal{H}(p^{\prime}(\cdot),q^{\prime},α^{\prime})$. Finally, we prove that neither $(L^{p(\cdot)}, \ell^{q})^α$ nor $\mathcal{H}(p^{\prime}(\cdot),q^{\prime},α^{\prime})$ is reflexive.
Comments24 pages
