Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 493-510

INTERPOLATION SPACES AND GENERALIZED LORENTZ–ZYGMUND SPACES

Blanca F. Besoy, Fernando Cobos and Luz M. Fernández-Cabrera

Universidad Complutense de Madrid, Facultad de Matemáticas
Departamento de Análisis Matemático y Matemática Aplicada
Plaza de Ciencias 3, 28040 Madrid, Spain; blanca.f.besoy 'at' ucm.es

Universidad Complutense de Madrid, Facultad de Matemáticas
Departamento de Análisis Matemático y Matemática Aplicada
Plaza de Ciencias 3, 28040 Madrid, Spain; cobos 'at' mat.ucm.es

Universidad Complutense de Madrid, Facultad de Estudios Estadísticos
Sección Departamental de Análisis Matemático y Matemática Aplicada
28040 Madrid, Spain; luz_fernandez-c 'at' mat.ucm.es

Abstract. We determine the associate space of the logarithmic interpolation space (X₀,X₁)_1,q,A where X₀ and X₁ are Banach function spaces over a σ-finite measure space (Ω,μ). Particularizing the results for the case of the couple (L₁,L_∞) over a non-atomic measure space, we recover results of Opic and Pick on associate spaces of generalized Lorentz–Zygmund spaces L_(∞,q;A). We also establish the corresponding results for sequence spaces.

2010 Mathematics Subject Classification: Primary 46B70, 46E30.

Key words: Banach function spaces, logarithmic interpolation spaces, description of K-spaces in terms of the J-functional, generalized Lorentz–Zygmund spaces.

Reference to this article: B. F. Besoy, F. Cobos and L. M. Fernández-Cabrera: Associate spaces of logarithmic interpolation spaces and generalized Lorentz–Zygmund spaces. Ann. Acad. Sci. Fenn. Math. 45 (2020), 493-510.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4525