论文标题
可变2-Microlocal besov型和Triebel-lizorkin型空间的非平滑原子分解
Non-smooth atomic decomposition of variable 2-microlocal Besov-type and Triebel-Lizorkin-type spaces
论文作者
论文摘要
在本文中，我们提供了2-微胶质besov-type和triebel-lizorkin-type空间的非平滑原子分解，带有可变指数的空间$ b^{\ mathrm {\boldsymbolΩ} $ f^{\ mathrm {\boldsymbolΩ}，ϕ} _ {p（\ cdot），q（\ cdot）}（\ mathbb {r}^n）$。一般而言，重要的是我们也提出的最大函数和本地手段的空间表征。这些空间最近由Wu在Al引入。并不仅覆盖可变2-Microcal besov和Triebel-lizorkin Spaces $ B^{\ Mathrm {\BoldSymbolΩ}} _ { $ f^{\ MATHRM {\BOLDSYMBOLΩ}} _ {p（\ cdot），q（\ cdot）}（\ Mathbb {r}^n）$，也是更经典的平滑度莫雷spaces $ b^{s，s，τ} _ { $ f^{s，τ} _ {p，q}（\ mathbb {r}^n）$。之后，我们在此量表上陈述了一个点式乘数断言。
In this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel-Lizorkin-type spaces with variable exponents $B^{\mathrm{\boldsymbolω}, ϕ}_{p(\cdot),q(\cdot)}(\mathbb{R}^n)$ and $F^{\mathrm{\boldsymbolω}, ϕ}_{p(\cdot),q(\cdot)}(\mathbb{R}^n)$. Of big importance in general, and an essential tool here, are the characterizations of the spaces via maximal functions and local means, that we also present. These spaces were recently introduced by Wu at al. and cover not only variable 2-microlocal Besov and Triebel-Lizorkin spaces $B^{\mathrm{\boldsymbolω}}_{p(\cdot),q(\cdot)}(\mathbb{R}^n)$ and $F^{\mathrm{\boldsymbolω}}_{p(\cdot),q(\cdot)}(\mathbb{R}^n)$, but also the more classical smoothness Morrey spaces $B^{s, τ}_{p,q}(\mathbb{R}^n)$ and $F^{s,τ}_{p,q}(\mathbb{R}^n)$. Afterwards, we state a pointwise multipliers assertion for this scale.
