论文标题
HERZ型Triebel-lizorkin空间上的组成操作员，并应用于半连接抛物线方程
Composition operators on Herz-type Triebel-Lizorkin spaces with application to semilinear parabolic equations
论文作者
论文摘要
令$ g：\ mathbb {r \ rightarrow r} $成为一个连续的函数。在本文的第一部分中，我们调查了$ g $的足够条件，以便 \ begin {equation*} \ {g（f）：f \ in \ dot {K} _ { \ end {equation*} 持有。这里$ \ dot {k} _ {p，q}^{α} f_ {β}^{s} $是herz-type triebel-lizorkin空间。这些空间统一并概括了许多经典的功能空间，例如功率重量的Lebesgue空间，Sobolev和Triebel-Lizorkin的功率权重。在本文的第二部分中，我们将研究半连接抛物线方程的本地和全球库奇问题 \ begin {equation*} \ partial _ {t} u-Δu= g（u） \ end {equation*} 在HERZ型Triebel-Lizorkin空间中具有初始数据。我们的结果涵盖了在某些已知功能空间中使用初始数据获得的结果，例如美国分数Sobolev空间。给出了一些限制案例。
Let $G:\mathbb{R\rightarrow R}$ be a continuous function. In the first part of this paper, we investigate sufficient conditions on $G$ such that \begin{equation*} \{G(f):f\in \dot{K}_{p,q}^{α}F_{β}^{s}\}\subset \dot{K}_{p,q}^{α}F_{β}^{s} \end{equation*} holds. Here $\dot{K}_{p,q}^{α}F_{β}^{s}$ are Herz-type Triebel-Lizorkin spaces. These spaces unify and generalize many classical function spaces such as Lebesgue spaces of power weights, Sobolev and Triebel-Lizorkin spaces of power weights. In the second part of this paper we will study local and global Cauchy problems for the semilinear parabolic equations \begin{equation*} \partial _{t}u-Δu=G(u) \end{equation*} with initial data in Herz-type Triebel-Lizorkin spaces. Our results cover the results obtained with initial data in some know function spaces such us fractional Sobolev spaces. Some limit cases are given.
