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Orlicz spaces associated to a quasi-Banach function space: applications to vector measures and interpolation
Collectanea Mathematica ( IF 1.1 ) Pub Date : 2020-07-02 , DOI: 10.1007/s13348-020-00295-1
Ricardo del Campo , Antonio Fernández , Fernando Mayoral , Francisco Naranjo

The Orlicz spaces \(X^{\varPhi }\) associated to a quasi-Banach function space X are defined by replacing the role of the space \(L^1\) by X in the classical construction of Orlicz spaces. Given a vector measure m, we can apply this construction to the spaces \(L^1_w(m),\)\(L^1(m)\) and \(L^1(\Vert m\Vert )\) of integrable functions (in the weak, strong and Choquet sense, respectively) in order to obtain the known Orlicz spaces \(L^{\varPhi }_w(m)\) and \(L^{\varPhi }(m)\) and the new ones \(L^{\varPhi }(\Vert m\Vert ).\) Therefore, we are providing a framework where dealing with different kind of Orlicz spaces in a unified way. Some applications to complex interpolation are also given.



中文翻译:

与拟Banach函数空间相关的Orlicz空间:矢量测度和插值的应用

与准Banach函数空间X相关的Orlicz空间\(X ^ {\ varPhi} \)是通过在Orlicz空间的经典构造中用X代替空间\(L ^ 1 \)的作用来定义的。给定一个向量度量m,我们可以将此构造应用于空间\(L ^ 1_w(m),\)\(L ^ 1(m)\)\(L ^ 1(\ Vert m \ Vert)\)(分别在弱,强和Choquet意义上)的积分函数,以获得已知的Orlicz空间\(L ^ {\ varPhi _w(m)\)\(L ^ {\ varPhi}(m)\ )和新的\(L ^ {\ varPhi}(\ Vert m \ Vert)。\)因此,我们提供了一个框架,以统一的方式处理不同种类的Orlicz空间。还给出了复杂插值的一些应用。

更新日期:2020-07-03
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