Duality for Interpolation Spaces Defined Via Slowly Varying Functions: The Case 0<q<1

P. FernÃ¡ndez-MartÃ­nez; M. Grover; T. M. Signes

paper

Duality for Interpolation Spaces Defined Via Slowly Varying Functions: The Case 0<q<1

arXiv:2606.19515

Abstract

Given $(A_{0}, A_{1})$ a compatible couple of Banach spaces, we describe the dual of the limiting real interpolation space $(A_{0}, A_{1})_{1, q, b}^{K}$ for $0 < q < 1$ and $b$ a slowly varying function. In the process, we use the $J$ -spaces $(A_{0}, A_{1})_{1, q, b}^{J}$ and we establish an equivalence theorem for $K$ and $J$ spaces of independent interest. We also give examples that recover known results on this topic.

16 pages