CAFFARELLI-KOHN-NIRENBERG INEQUALITIES FOR BESOV AND TRIEBEL-LIZORKIN-TYPE SPACES
CAFFARELLI-KOHN-NIRENBERG INEQUALITIES FOR BESOV AND TRIEBEL-LIZORKIN-TYPE SPACES
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 …