Interpolation and duality of generalized grand Morrey spaces on quasi-metric measure spaces

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Abstract

Let θ ∈ (0, 1), λ ∈ [0, 1) and p, p0, p1 ∈ (1,∞] be such that (1 − θ)/p0 + θ/p1 = 1/p, and let φ, φ0, φ1 be some admissible functions such that φ, φ0p/p0 and φ1p/p1 are equivalent. We first prove that, via the ± interpolation method, the interpolation Lφ0p0),λ (X), Lφ1p1), λ (X), θ> of two generalized grand Morrey spaces on a quasi-metric measure space X is the generalized grand Morrey space Lφp),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.

Keywords

grand Lebesgue space grand Morrey space Gagliardo-Peetre method quasimetric measure space Calderón product predual space ± interpolation method 

MSC 2010

46B70 46B10 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of EducationBeijing, HaidianPeople’s Republic of China

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