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

被引：7

作者：

Liu, Yi ^{[1
]}

Yuan, Wen ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, 19 Xinjiekouwai St, Beijing 100875, Haidian, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2017年 / 67卷 / 03期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

grand Lebesgue space; grand Morrey space; Gagliardo-Peetre method; quasi-metric measure space; Calderon product; predual space; +/- interpolation method; LEBESGUE SPACES; PARABOLIC EQUATIONS; RIESZ-POTENTIALS; SOBOLEV SPACES; INTEGRABILITY; REGULARITY; OPERATOR; THEOREM;

D O I：

10.21136/CMJ.2017.0081-16

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let theta a (0, 1), lambda a [0, 1) and p, p (0), p (1) a (1,a] be such that (1 - theta)/p (0) + theta/p (1) = 1/p, and let phi, phi(0), phi(1) be some admissible functions such that phi, phi(0) (p/p0) and phi(1) (p/p1) are equivalent. We first prove that, via the +/- interpolation method, the interpolation L (phi 0) (p0),lambda) (X), L (phi 1) (p1), lambda) (X), theta > of two generalized grand Morrey spaces on a quasi-metric measure space X is the generalized grand Morrey space L (phi) (p),lambda) (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.

引用

页码：715 / 732

页数：18

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