Interpolation and duality of generalized grand Morrey spaces on quasi-metric measure spaces |
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Authors: | Yi Liu Wen Yuan |
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Institution: | 1.School of Mathematical Sciences,Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education,Beijing, Haidian,People’s Republic of China |
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Abstract: | Let θ ∈ (0, 1), λ ∈ 0, 1) and p, p 0, p 1 ∈ (1,∞] be such that (1 ? θ)/p 0 + θ/p 1 = 1/p, and let φ, φ0, φ1 be some admissible functions such that φ, φ0 p/p0 and φ1 p/p1 are equivalent. We first prove that, via the ± interpolation method, the interpolation L φ0 p0),λ (X), L φ1 p1), λ (X), θ> of two generalized grand Morrey spaces on a quasi-metric measure space X is the generalized grand Morrey space L φ p),λ (X). Then, by using block functions, we also find a predual space of the generalized grand Morrey space. These results are new even for generalized grand Lebesgue spaces. |
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