Banach Journal of Mathematical Analysis

Interpolation with a parameter function of Lp-spaces with respect to a vector measure on a δ-ring

R. del Campo, A. Fernández, A. Manzano, F. Mayoral, and F. Naranjo

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Abstract

Let ν be a σ-finite Banach-space-valued measure defined on a δ-ring. We find a wide class of measures ν for which interpolation with a parameter function of couples of Banach lattices of p-integrable and weakly p-integrable functions with respect to ν 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
Received: 23 December 2015
Accepted: 27 January 2016
First available in Project Euclid: 30 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1475267149

Digital Object Identifier
doi:10.1215/17358787-3649590

Mathematical Reviews number (MathSciNet)
MR3553214

Zentralblatt MATH identifier
1366.46016

Subjects
Primary: 46B70: Interpolation between normed linear spaces [See also 46M35]
Secondary: 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22] 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
real interpolation vector measures integrable function spaces

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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References

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