Abstract:In this paper, based on generalized Herz-type function spaces $\dot{K}_{q}^{p}(\theta)$ were introduced by Y. Komori and K. Matsuoka in 2009, we define Herz-type Besov spaces $\dot{K}_{q}^{p}B_{\beta }^{s}(\theta)$ and Herz-type Triebel-Lizorkin spaces $\dot{K}_{q}^{p}F_{\beta }^{s}(\theta)$, which cover the Besov spaces and the Triebel-Lizorkin spaces in the homogeneous case, where $\theta=\left\{\theta(k)\right\} _{k\in\mathbb{Z}}$ is a sequence of non-negative numbers $\theta(k)$ such that \begin{equation*}… Show more
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