  We present some Caffarelli-Kohn-Nirenberg-type inequalities on Herz-type
Besov-Triebel-Lizorkin spaces, Besov-Morrey spaces and Triebel-Lizorkin-Morrey
spaces. More Precisely, we investigate the inequalities \begin{equation*}
\big\|f\big\|_{\dot{k}_{v,\sigma }^{\alpha_{1},r}}\leq
c\big\|f\big\|_{\dot{K}_{u}^{\alpha_{2},\delta }}^{1-\theta
}\big\|f\big\|_{\dot{K}_{p}^{\alpha_{3},\delta_{1}}A_{\beta }^{s}}^{\theta },
\end{equation*} and
  \begin{equation*} \big\|f\big\|_{\mathcal{E}_{p,2,u}^{\sigma }}\leq
c\big\|f\big\|_{\mathcal{M}_{\mu }^{\delta }}^{1-\theta
}\big\|f\big\|_{\mathcal{N}_{q,\beta ,v}^{s}}^{\theta }, \end{equation*} with
some appropriate assumptions on the parameters, where $\dot{k}_{v,\sigma
}^{\alpha_{1},r}$ is the Herz-type Bessel potential spaces, which are just the
Sobolev spaces if $\alpha_{1}=0,1<r=v<\infty $ and $% \sigma \in
\mathbb{N}_{0}$, and $\dot{K}_{p}^{\alpha_{3},\delta_{1}}A_{\beta }^{s}$ are
Besov or Triebel-Lizorkin spaces if $\alpha_{3}=0$ and$\ \delta_{1}=p$. To do
these, we study when distributions belonging to these spaces can be interpreted
as functions in $L_{\mathrm{loc}}^{1}$. The usual Littlewood-Paley technique,
Sobolev and Franke embeddings are the main tools of this paper. Some remarks on
Hardy-Sobolev inequalities are given.
