## Banach Journal of Mathematical Analysis

### Interpolation with a parameter function of $L^{p}$-spaces with respect to a vector measure on a $\delta$-ring

#### Abstract

Let $\nu$ be a $\sigma$-finite Banach-space-valued measure defined on a $\delta$-ring. We find a wide class of measures $\nu$ for which interpolation with a parameter function of couples of Banach lattices of $p$-integrable and weakly $p$-integrable functions with respect to $\nu$ produces a Lorentz-type space. Moreover, we prove that if we interpolate between sums and intersections of them, then they still yield another Lorentz-type space closely related with the first one.

#### Article information

Source
Banach J. Math. Anal., Volume 10, Number 4 (2016), 815-827.

Dates
Accepted: 27 January 2016
First available in Project Euclid: 30 September 2016

https://projecteuclid.org/euclid.bjma/1475267149

Digital Object Identifier
doi:10.1215/17358787-3649590

Mathematical Reviews number (MathSciNet)
MR3553214

Zentralblatt MATH identifier
1366.46016

#### Citation

del Campo, R.; Fernández, A.; Manzano, A.; Mayoral, F.; Naranjo, F. Interpolation with a parameter function of $L^{p}$ -spaces with respect to a vector measure on a $\delta$ -ring. Banach J. Math. Anal. 10 (2016), no. 4, 815--827. doi:10.1215/17358787-3649590. https://projecteuclid.org/euclid.bjma/1475267149

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