Normed Köthe space structure and Köthe duals of variable-exponent Fofana spaces and their preduals
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institution: Université Félix Houphouët-Boigny
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214049095