We continue the study of the variable exponent Morreyfied Triebel–Lizorkin spaces introduced in a previous paper. Here we give characterizations by means of atoms and molecules. We also show that in some cases the number of zero moments needed for molecules, in order that an infinite linear combination of them (with coefficients in a natural sequence space) converges in the space of tempered distributions, is much smaller than what is usually required. We also establish a Sobolev type theorem for related sequence spaces, which might have independent interest.

中文翻译：

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可变指数 Triebel-Lizorkin-Morrey 空间的原子和分子分解

我们继续研究前一篇论文中介绍的可变指数 Morreyfied Triebel-Lizorkin 空间。在这里，我们通过原子和分子来进行表征。我们还表明，在某些情况下，为了使分子的无限线性组合（具有自然序列空间中的系数）在调和分布空间中收敛，分子所需的零矩数量远小于通常所需的数量. 我们还为相关的序列空间建立了一个 Sobolev 类型定理，它可能具有独立的兴趣。