Complex interpolation of some Banach spaces including Morrey spaces

Document Type : Original Article

Authors

Nouffou Diarra ¹

Ibrahim Fofana ²

¹ Laboratoire de Mathematiques et Applications, UFR Mathematiques et Informatique, Universite Felix Houphouet Boigny, Abidjan-Cocody, 22 BP 582, Abidjan 22, Cote d'ivoire.

² Laboratoire de Mathematiques et Applications, UFR Mathematiques et Informatique, Uniiversite Felix Houphouet Boigny , Abidjan, Cote d' I voire

10.22034/kjm.2023.386475.2778

Abstract

Let $1≤q≤α≤∞$. The sets $\{(L^q,l^p )^α (\mathbb R^d ); α≤p≤∞\}$ and $\{F(q,p,α) (\mathbb R^d),; α≤p≤∞ \}$ are two nondecreasing families of Banach spaces such that for both the Lebsegue space $L^α(\mathbb R^d)$ is the minimal element and the Morrey space $M_q^α(\mathbb R^d)$ is the maximal element. It is also known that for $1<q≤α≤p≤∞$, $(L^q,l^p )^α (\mathbb R^d )$ has a predual space $H(q',p',α')(\mathbb R^d )$ which is also its Köthe dual space when $α<p$ . In this paper, we obtain complex interpolation theorems in the above mentioned three families of Banach spaces. Our results extend analogous ones recently obtained for Morrey spaces and their preduals.

Keywords

Complex interpolation

Morrey spaces

predual

Normed Köthe space,

Banach lattice

Subjects

• 46 Functional analysis

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