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Description of logarithmic interpolation spaces by means of the J-functional and applications

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Cobos, Fernando and Segurado, Alba (2015) Description of logarithmic interpolation spaces by means of the J-functional and applications. Journal of Functional Analysis, 268 (10). pp. 2906-2945. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123615001068


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Abstract

We work with logarithmic interpolation methods (A0,A1)θ,q,A where θ=0 or 1. On the contrary to the case 0<θ<1, we show that their description in terms of the J-functional changes depending on the relationship between q and A, and that there is no description in a certain range. Then we use these J -descriptions to investigate the behavior of compact operators and weakly compact operators under logarithmic interpolation methods. In particular, we extend a recent compactness result of Edmunds and Opic for operators between Lp-spaces over finite measure spaces to σ -finite measure spaces. We also determine the dual of (A0,A1)θ,q,A when θ=0 or 1.


Item Type:Article
Uncontrolled Keywords:Logarithmic interpolation methods; Compact operators; Lorentz–Zygmund spaces; Weakly compact operators
Subjects:Sciences > Mathematics
ID Code:30250
Deposited On:22 May 2015 08:27
Last Modified:22 May 2015 08:27

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