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October 2016 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, F. Naranjo
Banach J. Math. Anal. 10(4): 815-827 (October 2016). DOI: 10.1215/17358787-3649590

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.

Citation

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R. del Campo. A. Fernández. A. Manzano. F. Mayoral. F. Naranjo. "Interpolation with a parameter function of Lp-spaces with respect to a vector measure on a δ-ring." Banach J. Math. Anal. 10 (4) 815 - 827, October 2016. https://doi.org/10.1215/17358787-3649590

Information

Received: 23 December 2015; Accepted: 27 January 2016; Published: October 2016
First available in Project Euclid: 30 September 2016

zbMATH: 1366.46016
MathSciNet: MR3553214
Digital Object Identifier: 10.1215/17358787-3649590

Subjects:
Primary: 46B70
Secondary: 46E30, 46G10

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.10 • No. 4 • October 2016
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